Carl Pomerance

Phone: (603) 646-2635
Dept. Fax: (603) 646-1312
Office: 344 Kemeny Hall
Email: carl.pomerance@dartmouth.edu
US Mail: Department of Mathematics
Dartmouth College
Hanover, NH 03755-3551
(603) 646-2415

Brief CV


Books

  1. Lecture Notes on Primality Testing and Factoring: A Short Course at Kent State University, C. Pomerance, MAA Notes 4, Washington, DC, 1984.

  2. Advances in Cryptology: Crypto '87, C. Pomerance, ed., Lecture Notes in Computer Science 293, Springer–Verlag, Berlin, 1988.

  3. Cryptology and computational number theory, C. Pomerance, ed. Proc. Symp. Appl. Math. 42, Amer. Math. Soc., Providence, 1990.

  4. Prime numbers: a computational perspective, R. E. Crandall and C. Pomerance, Springer–Verlag, New York, 2001.

  5. Prime Numbers: a computational perspective, second edition, R. E. Crandall and C. Pomerance, Springer, New York, 2005. Errata.

  6. Topics in combinatorial number theory: Proceedings of the INTEGERS Conference 2003 in honor of Tom Brown, B. Landman, M. Nathanson, J. Nesetril, and C. Pomerance, eds., DIMATIA, Prague, 2005.

  7. Combinatorial Number Theory: Proceedings of the Integers Conference 2005 in Celebration of the 70th Birthday of Ron Graham, B. Landman, M. Nathanson, J. Nesetril, R. Nowakowski, and C. Pomerance, eds., De Gruyter, Berlin, 2007.

  8. Analytic number theory (in honor of Helmut Maier's 60th birthday), C. Pomerance and M. Rassias, eds., Springer, Cham, Switzerland, 2015.

  9. Analytic number theory (in honor of Helmut Maier's 70th birthday), J. Friedlander, C. Pomerance, and M. Rassias, eds., Springer, to appear.


Some Talks

  1. Covering talk, Talk on covering congruences (Joint Math Meetings, San Diego, January 2008).

  2. Undergrad covering talk, More elementary talk on covering congruences (Spuyten Duyvil Undergraduate Mathematics Meeting, New York City, April, 2008; Ohio and Michigan MAA Sections, Spring 2008).

  3. Talk on Euler's function, Talk at University of Georgia, February 2008 and Trinity University, March 2008.

  4. Elementary primality talk, Lucas Lecture at Fibonacci Association Meeting in Patras, Greece, July 2008.

  5. Fields talk, Counting Fields. At Canadian Number Theory Association Meeting in Waterloo, Canada, July 2008. Version for Berkeley Number Theory Seminar, February 2010.

  6. Multiplicative order talk, The multiplicative order mod n, on average. At the Quebec/Maine number theory conference at Laval University, Quebec, Canada, October, 2008.

  7. Order and chaos, At the PANTS meeting (yes, a "long PANTS talk"), University of South Carolina, Columbia, SC, December, 2008. Version of March, 2009, Brigham Young University. Version of April, 2009, University of Rochester.

  8. Sociable numbers: new developments on an ancient problem, Session on the Beauty and Power of Number Theory, Joint Mathematics Meetings, Washington, DC, January, 2009.
    Long version of March, 2009, Brigham Young University undergraduate colloquium.
    Long version of April, 2009, Lorentz Center, Leiden, The Netherlands.
    The first dynamical system? AMS Special Session, Boston College, April, 2013.

  9. A 1935 Erdős paper on prime numbers and Euler's function, at the AMS Central Section meeting, University of Illinois, Urbana, IL, March, 2009.
    Version of July, 2009, at the University of Montreal and at the 41st Conference on Combinatorics, Graph Theory and Computing, Version of December, 2009, at the West Coast Number Theory Conference.

  10. Discrete Logarithms, Dartmouth Number Theory Seminar, November 19, 2009.

  11. Fixed points for discrete logarithms, 41st Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, FL, March 2010.
    Related talk: The Pólya–Vinogradov inequality, Illinois Number Theory Conference in Honor of Harold Diamond, May 21, 2010.
    Related talk: Fixed points for discrete logarithms, ANTS IX, Nancy, France, July 19–23, 2010.

  12. Fibonacci integers, Banff conference in honor of Cam Stewart, May 31, 2010 to June 4, 2010.

  13. Counting in number theory, the Rademacher Lectures, U Penn, September, 2010:
    Elementary number theory,
    Finite cyclic groups,
    Fibonacci integers,
    Counting fields

  14. Two problems in combinatorial number theory,
    Number theory and its applications, Debrecen, Hungary, Oct. 4–8, 2010.

  15. Elliptic curves: applications and problems,
    IMA Abel Conference, Minneapolis, MN, January, 2011.

  16. Order and chaos,
    MSRI Arithmetic Statistics Introductory Workshop, Berkeley, CA, January/February, 2011.
    Undergrad version: Order and chaos,
    Hudson River Undergraduate Mathematics Conference, Skidmore College, Saratoga Springs, NY, April 16, 2011.
    Grad version: Order and chaos,
    Quebec Student Conference, University of Montreal, May 20, 2011.
    Short version: A problem of Arnold on the average multiplicative order,
    Maine/Quebec Number Theory Conference, University of Maine, October 1,2, 2011.
    Version of November, 2012
    Version of December, 2013

  17. Product-free sets of integers,
    Integers Conference, Carrollton, GA, October, 2011.
    Sums and products,
    Mathematics & Statistics Colloquium, U. Vermont, December 2, 2011.
    Boston Meetings version,
    Joint Mathematics Meetings, Boston, MA, 2012.
    UC Irvine colloquium, February 9, 2012.
    Sums and products International Number Theory Conference in memory of Alf van der Poorten, AM, March 15, 2012.
    Sums and products Dartmouth Mathematics Society, May 16, 2012.
    Sums and products U. Georgia VIGRE seminar, November 28, 2012.
    Sums and products, West Chester U., April 24, 2013, SUNY Albany, April 25, 2013.
    Sums and products, Arizona State U., February 27, 2014.
    Sums and products, Providence College, April 2, 2014.
    What we still don't know about addition and multiplication, Johns Hopkins Center for Talented Youth, May 4, 2013.
    What we still don't know about addition and multiplication, Richard and Louise Guy Lecture, University of Calgary, September 12, 2013.
    What we still don't know about addition and multiplication, Woods Lecture Series, Butler University, December 3, 2013.
    What we still don't know about addition and multiplication, Fuzzy Vance Lecture, Oberlin College, March 20, 2014.
    What we still don't know about addition and multiplication, Christie Lecture, Bowdoin College, April 7, 2014.
    What we still don't know about addition and multiplication, Bay Area Mathematical Adventures, Santa Clara University, January 23, 2015.

  18. Sets of monotonicity for Euler's function,
    West Coast Number Theory Conference, Asilomar Conference Center, Pacific Grove, CA, December, 2011.

  19. The range of Carmichael's function,
    AMS Sectional Meeting, U. Hawaii, Honolulu, March, 2012.

  20. Balanced subgroups of the multiplicative group,
    Dartmouth Number Theory Seminar, April 26, 2012.
    Balanced subgroups of the multiplicative group,
    CNTA, June, 2012.
    Balanced subgroups of the multiplicative group,
    Quebec/Maine Number Theory Conference, September, 2012.
    Balanced subgroups of the multiplicative group,
    Central Section AMS Meeting, U. Akron, Akron, OH, October, 2012.
    Balanced subgroups of the multiplicative group,
    Palmetto Number Theory Symposium, December 2, 2012.

  21. Some statistical problems concerning the arithmetic functions σ and ϕ,
    Joint Mathematics Meetings, Special Session on Arithmetic Statistics, San Diego, CA, January, 2013.

  22. Erdős, van der Corput, and the birth of covering congruences,
    Joint Mathematics Meetings, Special Session on Covering Congruences, San Diego, CA, January, 2013.

  23. Paul Erdős and the rise of statistical thinking in elementary number theory,
    Erdős Centennial Conference, Budapest, July 1–5, 2013.
    Paul Erdős and the rise of statistical thinking in elementary number theory,
    Version of 1/15/14 at the Joint Math Meetings, Baltimore.

  24. The set of values of an arithmetic function,
    Mathematical Congress of the Americas, Guanajuato, Mexico, August 9, 2013.
    The set of values of an arithmetic function,
    Integers Conference (marking the Erdős centennial), University of West Georgia, Carrollton, GA, October 23–27, 2013.
    The ranges of various familiar functions,
    CNTA XIII, Carleton University, Ottawa, Canada, June 20, 2014.
    The ranges of some familar arithmetic functions, Maine/Quebec Number Theory Conference, Orono, ME, October 3-4, 2015.

  25. Square values of Euler's function,
    SCHOLAR conference in honour of M. Ram Murty, University of Montreal, October 15–17, 2013.

  26. Amicable numbers,
    Illinois Conference in Memory of Felice and Paul Bateman and Heini Halberstam, June 5-7, 2014.
    Amicable numbers,
    Brown University Algebra Seminar, April 6, 2015.

  27. The statistics of elementary number theory,
    2014 NCTS Conference on the Impact of Computation in Number Theory, 30 July, 2014 to 3 August, 2014, National Tsing Hua University, Hsinchu, Taiwan.
    Statistics in elementary number theory,
    CRM Workshop on "Statistics and elementary number theory", Montreal, 15-19 September, 2014.

  28. The first function, U. Georgia colloquium, December 3, 2014.

    The first function, Middlebury College Seminar, April 21, 2015.

    The first function, Connections in Discrete Mathematics, A celebration of the work of Ron Graham, Simon Fraser U., June 15 - 19, 2015

    The sum-of-proper-divisors function, BC–MIT Number Theory Seminar, September 15, 2015.

    The first function, Cal State Chico Colloquium, February 5, 2016.

    The first function, Dartmouth Colloquium, May 26, 2016.

    The first function, Western Michigan U., Colloquium, October 14, 2016.

  29. The CRM Aisenstadt Chair Lectures, December 8–12, 2014, Montréal.
    The ranges of some familiar functions, December 8, 2014.
    The first function, December 11, 2014.
    Amicable numbers, December 12, 2014

  30. Letters from the master: my correspondence with Paul Erdős,
    Lecture at History of Mathematics Special Interest Group of the Mathematical Association of America,
    Joint Mathematics Meetings, San Antonio, TX, January 10, 2015.
    Here are some sample letters that are discussed near the end of the talk.

  31. Random number theory,
    Lecture at Random Roads: A celebration of Joel Spencer's 70th birthday, NYU, April 30, 2016.

  32. 'Rithmetic revisited: what we still don't know about + and ×,
    Math Encounters, National Museum of Mathematics, June 1, 2016.

  33. The first function and the Guy-Selfridge conjecture,
    CNTA Calgary, Guy Session, June 21, 2016.

  34. The first dynamical system (with a short feature),
    Summer school on fractal geometry and complex dimensions, Cal Poly San Luis Obispo, June 27, 2016.

  35. Why the ABC conjecture, Kummer classes and anabelian geometry, U. Vermont, September 10-11, 2016.

  36. Euclidean prime generators, Dartmouth Number Theory Seminar, October 4, 2016 and Integers Conference, U. West Georgia, October 6, 2016.
    Euclidean prime generators, West Coast Number Theory Conference, Pacific Grove, CA, December 2016.

  37. What we still don't know about addition and multiplication, Undergraduate Lecture Series, Michigan State U., October 11, 2016.

  38. The ranges of some familiar arithmetic functions, Michigan State U. Colloquium, October 13, 2016.
    The ranges of some familiar arithmetic functions, Max Planck Institute for Mathematics, November 2, 2016.
    The ranges of some familiar arithmetic functions, MSRI, May 7, 2017.

  39. The first dynamical system, Charles U. (Prague) Seminar, November 8, 2016.
    Random number theory, Charles U. (Prague) Colloquium, November 8, 2016.

  40. U. Georgia talks, March 22-28, 2017
    Random number theory,
    Euclidean prime generators,
    What we still don't know about addition and multiplication,
    The first dynamical system.

  41. New results on an ancient function,
    Maine/Quebec Number Theory Conference, October 14,15, 2017.
    New results on an ancient function,
    Joint Math Meetings 2018, San Diego, Special Session on Computational Methods in Combinatorics and Number Theory.

  42. The aliquot constant,
    West Coast Number Theory Conference, December 16-20, 2017.

  43. What we still don't know about addition and multiplication,
    Leonard C. Sulski Memorial Lecture and MAA Northeastern Section Dinner Meeting, College of the Holy Cross, Worcester, MA, April 23, 2018.

  44. The Erdős problem on primitive sets,
    CRM workshop on Probability in Number Theory, U. de Montreál, May 28, 2018. (See draft of paper on this topic with some updated results.)
    The Erdős problem on primitive sets,
    Integer Conference, Augusta, GA, October 3, 2018.
    The Erdős problem on primitive sets,
    West Coast Number Theory Conference, Chico, CA, December 15-19, 2018.
    The Erdős problem on primitive sets,
    Joint Mathematics Meetings, Baltimore, MD, January 15-19, 2019.

  45. Random number theory,
    CMS Summer Meeting, U. New Brunswick, June 4, 2018.

  46. What we still don't know about addition and multiplication,
    Evans–Bourdon Lecture, Washington & Lee U., October 9, 2018.

  47. Primality testing: then and now,
    Celebrating 75 years of Mathematics of Computation, ICERM, November 1–3, 2018, Providence.

  48. What we still don't know about addition and multiplication,
    Trjitzinsky Lecture 1, U. Illinois Urbana-Champaign, November 27, 2018.
    Random number theory,
    Trjitzinsky Lecture 2, U. Illinois Urbana-Champaign, November 28, 2018.
    Primality testing: then and now,
    Trjitzinsky Lecture 3, U. Illinois Urbana-Champaign, November 29, 2018.

  49. Primality testing: then and now,
    Boise State University, February 20, 2019.

  50. Erdős and primitive sets,
    Erdős Lecture Series, University of Memphis, September 12–15, 2019.

  51. Cyclotomic polynomials: problems and results,
    PaNTS XXXIII, Clemson, SC, December 14–15, 2019.

  52. Glasby's cyclotomic ordering conjecture,
    West Coast Number Theory Conference, Asilomar, December 16–20, 2019.

  53. The first function,
    Bay Area Mathematical Adventures, Santa Clara U., January 31, 2020.

  54. Is 73 the best number?,
    MAA Golden Section Meeting, Mills College, February 29, 2020.

  55. Symmetric primes,
    CANT, New York City (via Zoom), June 3, 2020.

  56. Practical numbers,
    Number Theory Web Seminar (via Zoom), August 13, 2020.

  57. Aliquot sequences,
    Unsolved Problems Conference: Celebrating the living legacy of the mathematics of Richard Guy,
    University of Calgary (via Zoom), October 2, 2020.

  58. Denominators of Bernoulli numbers,
    Dartmouth Number Theory Seminar (via Zoom), May 25, 2021.

  59. Is 73 the best number?,
    MAA Northeastern Section Meeting (via Zoom), June 5, 2021.

  60. Coprime matchings and permutations,
    Santa Clara Math and CS Department, April 12, 2022.

  61. Coprime permutations,
    Dartmouth College Combinatorics Seminar, May 17, 2022.

  62. Permutations and arithmetic,
    Number Theory Conference Debrecen, July 4 to 8, 2022.

  63. Permutations and arithmetic,
    A celebration of analytic number theory, a conference in honor of Andrew Granville, September 6, 2022.

  64. The Sieve of Eratosthenes and Rough Numbers,
    West Coast Number Theory Conference, December 16, 2022.

  65. Digits,
    Athens/Atlanta Number Theory Seminar, February 6, 2023, Athens, GA.

  66. Digits,
    Arithmetic, Algebra, and Algorithms, ICMS, April 10–14, 2023, Edinburgh, Scotland.

  67. What we still don't know about addition and multiplication,
    Ross Program, July 18, 2023, Indiana and Ohio.

  68. The shifted-prime divisor function, PaNTS XXXVI (in memory of Kevin James), Clemson, October 21–22, 2023.

  69. Matchable numbers, CANT, CUNY, May 2024.

  70. Cyclotomic primes, Dartmouth Algebra/Number Theory Seminar, November 2024.


Papers

  1. Odd perfect numbers are divisible by at least seven distinct primes, C. Pomerance, Acta Arith. 25 (1974), 265–300.

  2. On Carmichael's conjecture, C. Pomerance, Proc. Amer. Math. Soc. 43 (1974), 297–298.

  3. A search for elliptic curves with large rank, D.E. Penney and C. Pomerance, Math. Comp. 28 (1974), 851–853.

  4. 714 and 715, C. Nelson, D.E. Penney, and C. Pomerance, J. Rec. Math. 7 (1974), 87–89.

  5. Three elliptic curves with rank at least seven, D.E. Penney and C. Pomerance, Math. Comp. 29 (1975), 965–967.

  6. The second largest prime factor of an odd perfect number, C. Pomerance, Math. Comp. 29 (1975), 914–921.

  7. On the congruences σ(n ) ≡ a (mod n ) and n ≡ a (mod ϕ(n )), C. Pomerance, Acta Arith. 26 (1975), 265–272.

  8. On an interesting property of 112359550561797752809, J.L. Hunsucker and C. Pomerance, Fibonacci Quarterly 13 (1975), 331–333.

  9. There are no odd super perfect numbers less than 7 x 1024, J.L. Hunsucker and C. Pomerance, Indian J. Math. 17 (1975), 107–120.

  10. Some new results on odd perfect numbers, G.G. Dandapat, J.L. Hunsucker, and C. Pomerance, Pacific J. Math. 57 (1975), 359–364.

  11. On multiply perfect numbers with a special property, C. Pomerance, Pacific J. Math. 57 (1975), 511–517.

  12. On composite n for which ϕ(n )|n –1, I, C. Pomerance, Acta Arith. 28 (1976), 387–389.

  13. Multiply perfect numbers, Mersenne primes and effective computability, C. Pomerance, Math. Ann. 226 (1977), 195–206.

  14. On a tiling problem of R. B. Eggleton, C. Pomerance, Discrete Math. 18 (1977), 63–70.

  15. On composite n for which ϕ(n )|n –1, II, C. Pomerance, Pacific J. Math. 69 (1977), 177–186.

  16. On the distribution of amicable numbers, C. Pomerance, J. reine angew. Math. 293/294 (1977), 217–222.

  17. On the largest prime factors of n and n +1, P. Erdős and C. Pomerance, Aequationes Math. 17 (1978), 311–321.

  18. On a class of relatively prime sequences, P. Erdős, D.E. Penney, and C. Pomerance, J. Number Theory 10 (1978), 451–474.

  19. The prime number graph, C. Pomerance, Math. Comp. 33 (1979), 399–408.

  20. On a problem of Evelyn–Linfoot and Page in additive number theory, C. Pomerance and D. Suryanarayana, Publ. Math. Debrecen 26 (1979), 237–244.

  21. Nearly parallel vectors, H.G. Diamond and C. Pomerance, Mathematika 26 (1979), 258–268.

  22. Some number theoretic matching problems, C. Pomerance, Proceedings of the Queen's Number Theory Conference, P. Ribenboim, ed., Queen's Papers in Pure and Applied Mathematics, No. 54, Kingston, Canada, 1979, 237–247.

  23. Collinear subsets of lattice point sequences — an analogue of Szemerédi's theorem, C. Pomerance, J. Combinatorial Theory (A) 28 (1980), 140–149.

  24. A note on the least prime in an arithmetic progression, C. Pomerance, J. Number Theory 12 (1980), 218–223.

  25. The pseudoprimes to 25 x 109, C. Pomerance, J.L. Selfridge, and S.S. Wagstaff, Jr., Math. Comp. 35 (1980), 1003–1026.

  26. Matching the natural numbers up to n with distinct multiples in another interval, P. Erdős and C. Pomerance, Nederl. Akad. Wetensch. Proc. Ser. A 83 (1980), 147–161.

  27. Proof of D.J. Newman's coprime mapping conjecture, C. Pomerance and J.L. Selfridge, Mathematika 27 (1980), 69–83.

  28. Popular values of Euler's function, C. Pomerance, Mathematika 27 (1980), 84–89.

  29. Sets on which an entire function is determined by its range, H.G. Diamond, C. Pomerance, and L. Rubel, Math. Z. 176 (1981), 383–398.

  30. On the distribution of amicable numbers, II, C. Pomerance, J. reine angew. Math. 325 (1981), 183–188.

  31. The arithmetic mean of the divisors of an integer, P.T. Bateman, P. Erdős, C. Pomerance, and E.G. Straus, Analytic Number Theory Proceedings, Philadelphia 1980, M. I. Knopp, ed., Lecture Notes in Math. 899 (1981), 197–220.

  32. On the distribution of pseudoprimes, C. Pomerance, Math. Comp. 37 (1981), 587–593.

  33. Recent developments in primality testing, C. Pomerance, Math. Intelligencer 3 (1981), 97–105.

  34. A new lower bound for the pseudoprime counting function, C. Pomerance, Illinois J. Math. 26 (1982), 4–9.

  35. The search for prime numbers, C. Pomerance, Scientific American 247 No. 6 (1982), 136–144.

  36. Analysis and comparison of some integer factoring algorithms, C. Pomerance, Computational Methods in Number Theory, Part I, H.W. Lenstra, Jr. and R. Tijdeman, eds., Math. Centre Tract 154, Amsterdam, 1982, 89–139.

  37. On distinguishing prime numbers from composite numbers, L.M. Adleman, C. Pomerance, and R.S. Rumely, Annals Math. 117 (1983), 173–206.

  38. An analogue of Grimm's problem of finding distinct prime factors of consecutive integers, P. Erdős and C. Pomerance, Utilitas Math. 24 (1983), 45–65.

  39. On a problem of Oppenheim concerning `Factorisatio Numerorum', E.R. Canfield, P. Erdős, and C. Pomerance, J. Number Theory 17 (1983), 1–28.

  40. Implementation of the continued fraction integer factoring algorithm, C. Pomerance and S.S. Wagstaff, Jr., Congressus Numerantium 37 (1983), 99–117.

  41. On the longest simple path in the divisor graph, C. Pomerance, Proc. Southeastern Conf. Combinatorics, Graph Theory, and Computing, Boca Raton, Florida, 1983, Cong. Num. 40 (1983), 291–304.

  42. Moduli r for which there are many small primes congruent to a modulo r, P.T. Bateman and C. Pomerance, Publ. Math. d'Orsay 83.04 (1983), 8–19.

  43. Lecture notes on primality testing and factoring — A short course at Kent State University, C. Pomerance, (based on notes by S. M. Gagola, Jr.), MAA Notes 4 (1984).

  44. Are there counter-examples to the Baillie—PSW primality test, in DOPO LE PAROLE aangeboden aan DR. A. K. LENSTRA, H. W. Lenstra, jr, J. K. Lenstra, and P. van Emde Boas, eds., Amsterdam, 1984. (Re-typeset by Jon Grantham.)

  45. New ideas for factoring large integers, C. Pomerance, J. W. Smith, and S. S. Wagstaff, Jr., Advances in Cryptology, Proc. Crypto 83, D. Chaum, ed., Plenum Press, New York, 1984, 81–85.

  46. Estimates for certain sums involving the largest prime factor of an integer, A. Ivic and C. Pomerance, Proc. Colloquium on Number Theory 34 (1981), Topics in Classical Number Theory, North Holland, 1984, 769–789.

  47. On the size of the coefficients of the cyclotomic polynomial, P. T. Bateman, C. Pomerance, and R. C. Vaughan, Proc. Colloquium on Number Theory 34 (1981), Topics in Classical Number Theory, North Holland, 1984, 171–202.

  48. View obstruction problems, III, T. W. Cusick and C. Pomerance, J. Number Theory 19 (1984), 131–139.

  49. The normal number of prime factors of ϕ(n ), P. Erdős and C. Pomerance, Rocky Mtn. J. Math. 15 (1985), 343–352.

  50. On locally repeated values of certain arithmetic functions, I, P. Erdős, C. Pomerance, and A. Sárközy, J. Number Theory 21 (1985), 319–332.

  51. Multiplicative relations for sums of initial k-th powers, D. E. Penney and C. Pomerance, Amer. Math. Monthly 92 (1985), 729–731.

  52. On the distribution of round numbers, C. Pomerance, Number Theory Proceedings, Ootacamund, India 1984, K. Alladi, ed., Lecture Notes in Math. 1122 (1985), 173–200.

  53. The quadratic sieve factoring algorithm, C. Pomerance, Advances in Cryptology, Proceedings of Eurocrypt 84, Paris, 1984, T. Beth. N. Cot, and I. Ingemarsson, eds., Lecture Notes in Computer Sci. 209 (1985), 169–182.

  54. On the Schnirelmann and asymptotic densities of certain sets of non-mulitples, P. Erdős, C. B. Lacampagne, C. Pomerance, and J. L. Selfridge, Proceedings of the Southeast Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, Florida, 1985, Congressus Numerantium 48 (1985), 67–79.

  55. On sums involving reciprocals of the largest prime factor of an integer, P. Erdős, A. Ivic, and C. Pomerance, Glasnik Math. 21 (1986), 283–300.

  56. On the number of false witnesses for a composite number, P. Erdős and C. Pomerance, Math. Comp. 46 (1986), 259–279.

  57. On primitive divisors of Mersenne numbers, C. Pomerance Acta Arith. 46 (1986), 355–367.

  58. On the distribution of the values of Euler's function, C. Pomerance, Acta Arith. 47 (1986), 63–70.

  59. On locally repeated values of certain arithmetic functions, II, P. Erdős, C. Pomerance, and A. Sárközy, Acta Math. Hungarica 49 (1987), 251–259.

  60. On the average number of groups of square-free order, C. Pomerance, Proc. Amer. Math. Soc. 99 (1987), 223–231.

  61. The smallest n-uniform hypergraph with positive discrepancy, N. Alon, D. J. Kleitman, C. Pomerance, M. Saks, and P. Seymour, Combinatorica 7 (1987), 151–160.

  62. On locally repeated values of certain arithmetic functions, III, P. Erdős, C. Pomerance, and A. Sárközy, Proc. Amer. Math. Soc. 101 (1987), 1–7.

  63. Very short primality proofs, C. Pomerance, Math. Comp. 48 (1987), 315–322.

  64. Fast, rigorous factorization and discrete logarithm algorithms, C. Pomerance, Discrete algorithms and complexity, D. S. Johnson, T. Nishizeki, A. Nozaki, H. S. Wilf, eds., Academic Press, Orlando, Florida, 1987, pp. 119–143.

  65. On products of sequences of integers, C. Pomerance and A. Sárközy, Coll. Math. Soc. Janos Bolyai 51 (1987), 447–463.

  66. A pipeline architecture for factoring large integers with the quadratic sieve algorithm, C. Pomerance, J. W. Smith, and R. Tuler, SIAM J. Comput. 17 (1988), 387–403.

  67. On homogeneous multiplicative hybrid problems in number theory, C. Pomerance and A. Sárközy, Acta Arith. 49 (1988), 291–302.

  68. On the number of distinct values of Euler's ϕ-function, H. Maier and C. Pomerance, Acta Arith. 49 (1988), 263–275.

  69. On divisors of sums of integers, III, C. Pomerance, A. Sárközy, and C. L. Stewart, Pacific J. Math. 133 (1988), 363–379.

  70. The generation of random numbers that are probably prime, P. Beauchemin, G. Brassard, C. Crépeau, C. Goutier, and C. Pomerance, Journal of Cryptology 1 (1988), 53–64.

  71. Two methods in elementary analytic number theory, C. Pomerance, Number theory and applications, R. A. Mollin, ed., Kluwer Academic Publishers, Dordrecht, 1989, pp. 135–161.

  72. On the composition of the arithmetic functions σ and ϕ, C. Pomerance, Colloq. Math. 58 (1989), 11–15.

  73. The probability that a random probable prime is composite, S.H. Kim and C. Pomerance, Math. Comp. 53 (1989), 721–741.

  74. Fonction zêta de Riemann et conjecture de Weyl–Berry pour les tambours fractals, M. L. Lapidus and C. Pomerance, C. R. Acad. Sci. Paris (Ser. I) 310 (1990), 343–348.

  75. On the normal behavior of the iterates of some arithmetic functions, P. Erdős, A. Granville, C. Pomerance, and C. Spiro, Analytic Number Theory, Proc. Conf. in honor of Paul T. Bateman, B. C. Berndt, et al. eds., Birkhauser, Boston, 1990, pp. 165–204.

  76. Unusually large gaps between consecutive primes, H. Maier and C. Pomerance, Trans. Amer. Math. Soc. 322 (1990), 201–237.

  77. On the least prime in certain arithmetic progressions, A. Granville and C. Pomerance, J. London Math. Soc. (2) 41 (1990), 193–200.

  78. Factoring, C. Pomerance, Cryptology and Computational Number Theory, C. Pomerance, ed., Proc. Symp. Appl. Math. 42, Amer. Math. Soc. Providence, 1990.

  79. Cryptology and computational number theory — an introduction, C. Pomerance, Cryptology and Computational Number Theory, C. Pomerance, ed., Proc. Symp. Appl. Math. 42, Amer. Math. Soc., Providence, 1990.

  80. On a theorem of Besicovitch: values of arithmetic functions that divide their arguments, P. Erdős and C. Pomerance, Indian J. Math. 32 (1990), 279–287.

  81. On prime divisors of Mersenne numbers, P. Erdős, P. Kiss, and C. Pomerance, Acta Arith. 57 (1991), 267–281.

  82. Carmichael's lambda function, P. Erdős, C. Pomerance, and E. Schmutz, Acta Arith. 58 (1991), 363–385.

  83. The distribution of Lucas and elliptic pseudoprimes, D.M. Gordon and C. Pomerance, Math. Comp. 57 (1991), 825–838.

  84. Grandes déviations pour certaines fonctions arithmétiques, M. Balazard, J.L. Nicolas, C. Pomerance, and G. Tenenbaum, J. Number Theory 40 (1992), 146–164.

  85. The distribution of smooth numbers in arithmetic progressions, A. Balog and C. Pomerance, Proc. Amer. Math. Soc. 115 (1992), 33–43.

  86. A rigorous time bound for factoring integers, H. W. Lenstra, Jr. and C. Pomerance, J. Amer. Math. Soc. 5 (1992), 483–516.

  87. Reduction of huge, sparse matrices over a finite field via created catastrophes, C. Pomerance and J. W. Smith, Experimental Math. 1 (1992), 90–94.

  88. The Riemann zeta function and the one dimensional Weyl-Berry conjecture for fractal drums, M. L. Lapidus and C. Pomerance, Proc. London Math. Soc. (3) 66 (1993), 41–69.

  89. Average case error estimates for the strong probable prime test, I. Damgard, P. Landrock, and C. Pomerance, Math. Comp. 61 (1993), 177–194.

  90. Carmichael numbers, C. Pomerance, Nieuw Arch. Wisk. 11 (1993), 199–209.

  91. On elements of sumsets with many prime factors, P. Erdős, C. Pomerance, A. Sárközy, and C. L. Stewart, J. Number Theory 44 (1993), 93–104.

  92. An upper bound in Goldbach's conjecture, J.M. Deshouillers, A. Granville, W. Narkiewicz, and C. Pomerance, Math. Comp. 61 (1993), 209–213.

  93. Factoring integers with the number field sieve, J. Buhler, H. W. Lenstra, Jr., and C. Pomerance, The development of the number field sieve, A. K. Lenstra and H. W. Lenstra, Jr., eds., Lecture Notes in Math. 1554, pp. 50–94, Springer-Verlag, Berlin, 1993.

  94. A hyperelliptic smoothness test. I, H. W. Lenstra, Jr., J. Pila, and C. Pomerance, Phil. Trans. R. Soc. London A 345 (1993), 397–408.

  95. Sixes and sevens, C. Pomerance, Missouri J. Math. Sci. 6 (1994), 62–63.

  96. There are infinitely many Carmichael numbers, W. R. Alford, A. Granville, and C. Pomerance, Ann. of Math. (2) 139 (1994), 703–722.

  97. On the difficulty of finding reliable witnesses, W. R. Alford, A. Granville, and C. Pomerance, Algorithmic Number Theory Proceedings (ANTS-I), L. M. Adleman and M.-D. Huang, eds., Lecture Notes in Computer Sci. 877 (1994), Springer-Verlag, Berlin, pp. 1–16.

  98. Dickson polynomials with few fixed points in a finite field, C. Pomerance, J. Sichuan U. (Natural Science Ed.) 31 (1994), 460–464.

  99. On a conjecture of R. L. Graham, F. Y. Cheng and C. Pomerance, Rocky Mtn. J. Math. 24 (1994), 961–975.

  100. The number field sieve, C. Pomerance, Mathematics of Computation, 1943–1993, Fifty Years of Computational Mathematics, W. Gautschi, ed., Proc. Symp. Appl. Math. 48, American Mathematical Society, Providence, 1994, pp. 465–480.

  101. Counting the integers factorable via cyclotomic methods, C. Pomerance and J. Sorenson, J. Algorithms, 19 (1995), 250–265.

  102. On a conjecture of Crandall concerning the qx +1 problem, Z. Franco and C. Pomerance, Math. Comp. 64 (1995), 1333–1336.

  103. Implementing the self initializing quadratic sieve on a distributed network, W.R. Alford and C. Pomerance, Number Theoretic and Algebraic Methods in Computer Science, Proc. of Int'l Moscow Conference, June-July, 1993, A. J. van der Poorten, I. Shparlinski, H. G. Zimmer, eds., World Scientific, 1995, pp. 163–174.

  104. Combinatorial number theory, C. Pomerance and A. Sárközy, Handbook of Combinatorics, R. L. Graham, M. Grötschel, L. Lovász, eds., Elsevier Science B.V., 1995, pp. 967–1018.

  105. On the role of smooth numbers in number theoretic algorithms, C. Pomerance, Proceedings of the Intenational Congress of Mathematicians, Zurich, Switzerland 1994, Birkhauser Verlag, Basel, 1995, pp. 411–422.

  106. Counterexamples to the modified Weyl-Berry conjecture, M.L. Lapidus and C. Pomerance, Math. Trans. Cambridge Phil. Soc. 119 (1996), 167–178.

  107. Symmetric and asymmetric primes, P. Fletcher, W. Lindgren, and C. Pomerance, J. Number Theory 58 (1996), 89–99.

  108. Multiplicative independence for random integers, C. Pomerance, Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, Vol. 2, B. Berndt, H. Diamond, A. Hildebrand, eds., Birkhauser, Boston, 1996, pp. 703–711.

  109. On the divisors of n !, P. Erdős, S.W. Graham, A. Ivic, and C. Pomerance, Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, Vol. 1, B. Berndt, H. Diamond, A. Hildebrand, eds., Birkhauser, Boston, 1996, pp. 337–355.

  110. A tale of two sieves, C. Pomerance, The Notices of the Amer. Math. Soc. 43 (1996), 1473–1485.

  111. On primes recognizable in deterministic polynomial time, S. V. Konyagin and C. Pomerance, The mathematics of Paul Erdős, R. L. Graham and J. Nesetril, eds., Springer-Verlag, Berlin, 1997, pp. 176–198.
    See #188 for an update article.

  112. A search for Wieferich and Wilson primes, R. Crandall, K. Dilcher, and C. Pomerance, Math. Comp. 66 (1997), 433–449.

  113. On locally repeated values of certain arithmetic functions, IV, P. Erdős, C. Pomerance, and A. Sárközy, The Ramanujan J. 1 (1997), 227–241.

  114. Automaticity II: Descriptional complexity in the unary case, C. Pomerance, J.M. Robson, and J. Shallit, Theoretical Computer Sci. 180 (1997), 181–201.

  115. Paul Erdős, number theorist extraordinaire, C. Pomerance, The Notices of the Amer. Math. Soc. 45 (1998), 19–23.

  116. Rigorous discrete logarithm computations in finite fields via smooth polynomials, R. Lovorn Bender and C. Pomerance, AMS/IP Studies in Advanced Mathematics 7 (1998), 221–232.

  117. Euler's function in residue classes, T. Dence and C. Pomerance, The Ramanujan Journal 2 (1998), 7–20.

  118. On the distribution of champs, A. Ivic and C. Pomerance, Proceedings of the Fifth Conference of the Canadian Number Theory Association, R. Gupta and K.S. Williams, eds., CRM Proc. 19 (1999), 133–139.

  119. Residue classes free of values of Euler's function, K. Ford, S. V. Konyagin, and C. Pomerance, Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 805–812.

  120. On the solutions to ϕ(n ) = ϕ(n +k ), S.W. Graham, J.J. Holt, and C. Pomerance, Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 867–882.

  121. Primes and factorization, J. Grantham and C. Pomerance, Handbook of Discrete Mathematics, K.H. Rosen, ed., CRC Press, 1999.

  122. Small values of the Carmichael function and cryptographic applications, J. Friedlander, C. Pomerance, and I. E. Shparlinski, Proc. Workshop on Cryptography and Computational Number Theory (CCNT'99), K.-Y. Lam, I. E. Shparlinski, H. Wang, and C. Xing, eds., Birkhäuser, 2001, pp. 25–32.

  123. The expected number of random elements to generate a finite abelian group, C. Pomerance, Periodica Mathematica Hungarica 43 (2001), 191–198.

  124. Period of the power generator and small values of the Carmichael function, J. Friedlander, C. Pomerance, and I. E. Shparlinski, Math. Comp., 70 (2001), 1591–1605. Corrigendum, op. cit., 71 (2002), 1803–1806.

  125. Two contradictory conjectures concerning Carmichael numbers, A. Granville and C. Pomerance, Math. Comp., 71 (2001), 883–908.

  126. On the problem of uniqueness for the maximal Stirling number(s) of the second kind, E.R. Canfield and C. Pomerance, Integers, 2 (2002), paper A1, 13 pp.
    (The published form of this paper was somewhat corrupted. The version here also corrects a small error in Section 4. Posted February, 2013.)

  127. On some problems of Makowski–Schinzel and Erdős concerning the arithmetical functions ϕ and σ, F. Luca and C. Pomerance, Colloq. Math., 92 (2002), 111–130. See also this.

  128. Smooth orders and cryptographic applications, C. Pomerance and I.E. Shparlinski, Proc. ANTS-V, Sydney, Australia, Springer Lecture Notes in Computer Science 2369, (2002), pp. 338–348.

  129. A hyperelliptic smoothness test. II, H. W. Lenstra, Jr., J. Pila, and C. Pomerance, Proc. London Math. Soc., (3) 84 (2002), 105–146.

  130. Ruth–Aaron numbers revisited, C. Pomerance, Paul Erdős and his Mathematics, (Budapest, 1999), Bolyai Soc. Math. Stud. 11, János Bolyai Math. Soc., Budapest, 2002, pp. 567–579.

  131. Primitive roots: a survey, S. Li and C. Pomerance, in New Aspects of Analytic Number Theory (RIMS Kokyuroku No. 1274) (Y. Tanigawa, ed.), and also in Dev. Math. 8, pp. 219–231, Kluwer Academic Publishers, Dordrecht 2002.

  132. On generalizing Artin's conjecture on primitive roots to composite moduli, S. Li and C. Pomerance, J. Reine Angew. Math. 556 (2003), 205–224.

  133. Timed fair exchange of arbitrary signatures, J. A. Garay and C. Pomerance, in Financial Cryptography, 7th International Conference, FC 2003, Lecture Notes in Computer Science 2742, Springer, New York, 2003, pp. 190–207.

  134. Multiplicative structure of values of the Euler function, W. D. Banks, J. B. Friedlander, C. Pomerance, and I. E. Shparlinski, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), pp. 29–47.

  135. Heuristics for class numbers of prime-power real cyclotomic fields, J. Buhler, C. Pomerance, and L. Robertson, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), pp. 149–157.

  136. Prime numbers and the search for extraterrestrial intelligence, C. Pomerance, in Mathematical Adventures for Students and Amateurs, D. Hayes and T. Shubin, eds., M.A.A., 2004, pp. 1–4.

  137. The largest prime factor of a Mersenne number, L. Murata and C. Pomerance, in Number Theory, CNTA Proceedings, Montreal, 2002, CRM Proc. Lecture Notes, 36, Amer. Math. Soc., Providence, RI, 2004, pp. 209–218.

  138. On the binary expansions of algebraic numbers, D. H. Bailey, J. M. Borwein, R. E. Crandall, and C. Pomerance, J. Théorie des Nombres Bordeaux 16 (2004), 487–518.

  139. On the distribution in residue classes of integers with a fixed sum of digits, C. Mauduit, C. Pomerance, and A. Sárközy), Ramanujan J., special issue in honor of J.-L. Nicolas 9 (2005), 45–62.

  140. Products of ratios of consecutive integers, R. de la Bretèche, C. Pomerance, and G. Tenenbaum, Ramanujan J., special issue in honor of J.-L. Nicolas 9 (2005), 131–138.

  141. The iterated Carmichael λ-function and the number of cycles of the power generator, G. Martin and C. Pomerance, Acta Arith. 118 (2005), 305–335.

  142. On the period of the linear congruential and power generators, P. Kurlberg and C. Pomerance, Acta Arith. 119 (2005), 149–169. Extended abstract with title "Lower bounds on the period of some pseudorandom number generators". In Proceedings of Conference on Algorithmic Number Theory 2007, vol. 46 of TUCS Gen. Pub., pages 74–81. Turku Cent. Comput. Sci., Turku, Finland, 2007. .

  143. Finding the group structure of elliptic curves over finite fields, J. B. Friedlander, C. Pomerance, and I. E. Shparlinski, Bull. Austral. Math. Soc. 72 (2005), 251–263.

  144. On the average number of divisors of the Euler function, F. Luca and C. Pomerance, Publ. Math. Debrecen, 70 (2007), 125–148.
    Corrigendum, submitted for publication.

  145. Sieving by large integers and covering systems of congruences, M. Filaseta, K. Ford, S. V. Konyagin, C. Pomerance, and G. Yu, J. Amer. Math. Soc., 20 (2007), 495–517.

  146. Maximal height of divisors of xn  –1, C. Pomerance and N. C. Ryan, Illinois J. Math., 51 (2007), 597–604.

  147. Irreducible radical extensions and Euler-function chains, F. Luca and C. Pomerance, pp. 351–362 in Combinatorial Number Theory, Landman et al., eds., de Gruyter, 2007, and in Integers, 7(2) (2007), paper A25.

  148. Smooth numbers and the quadratic sieve, C. Pomerance, in Algorithmic number theory, J. P. Buhler and P. Stevenhagen, eds., Math. Sci. Res. Inst. Pub. 44, Cambridge U. Press, New York, 2008, pp. 69–81.

  149. Elementary thoughts on discrete logarithms, C. Pomerance, in Algorithmic number theory, J. P. Buhler and P. Stevenhagen, eds., Math. Sci. Res. Inst. Pub. 44, Cambridge U. Press, New York, 2008, pp. 385–396.

  150. Computational number theory, C. Pomerance, in Princeton Companion to Mathematics, W. T. Gowers, ed., Princeton U. Press, Princeton, New Jersey, 2008, pp. 348–362.

  151. On the proportion of numbers coprime to a given integer, P. Erdős, F. Luca, and C. Pomerance, Proceedings of the Anatomy of Integers Conference, Montreal, March 2006, J.-M. De Koninck, A. Granville, F. Luca, eds., CRM Proceedings and Lecture Notes, vol. 46 (2008), 47–64.

  152. Sets with prescribed arithmetic densities, F. Luca, C. Pomerance, and S. Porubsky, Uniform Distribution Theory, 3 (2008), 67–80.

  153. On pseudosquares and pseudopowers, C. Pomerance and I. E. Shparlinski, Combinatorial Number Theory, Proceedings of Integers Conference 2007, de Gruyter, Berlin, 2009, pp. 171–184.

  154. On the range of the iterated Euler function, F. Luca and C. Pomerance, Combinatorial Number Theory, Proceedings of Integers Conference 2007, de Gruyter, Berlin, 2009, pp. 101–116.

  155. On Giuga numbers, F. Luca, C. Pomerance, and I. E. Shparlinski, Int. J. Mod. Math., 4 (2009), 13–28.

  156. On the distribution of sociable numbers, M. Kobayashi, P. Pollack, and C. Pomerance, J. Number Theory 129 (2009), 1990–2009.

  157. On the Artin–Carmichael primitive root problem on average, S. Li and C. Pomerance, Mathematika 55 (2009), 167–176.

  158. On the smallest pseudopower, J. Bourgain, S. V. Konyagin, C. Pomerance, and I. E. Shparlinski, Acta Arith. 140 (2009), 43–55.

  159. A remark on Giuga's conjecture and Lehmer's totient problem, W. D. Banks, C. W. Nevans, and C. Pomerance, Albanian J. Math. 3 (2009), 81–85.

  160. On the distribution of pseudopowers, S. V. Konyagin, C. Pomerance, and I. E. Shparlinski, Canad. J. Math., 62 (2010), 582–594.

  161. Rank statistics for a family of elliptic curves over a function field, C. Pomerance and I. E. Shparlinski, Pure Appl. Math. Q., 6 (2010), 21–40.

  162. Primality testing: variations on a theme of Lucas, C. Pomerance, in the Proceedings of the 13th Meeting of the Fibonacci Association, Congressus Numerantium 201 (2010), 301–312.

  163. Error estimates for the Davenport–Heilbronn theorems, K. Belabas, M. Bhargava, and C. Pomerance, Duke Math. J. 153 (2010), 173–210.

  164. Common values of the arithmetic functions ϕ and σ, K. Ford, F. Luca, and C. Pomerance, Bull. London Math. Soc., 42 (2010), 478–488.

  165. On Carmichael numbers in arithmetic progressions, W. D. Banks and C. Pomerance, J. Australian Math. Soc., 28 (2010), 313–321.

  166. On the radical of a perfect number, F. Luca and C. Pomerance, New York Journal of Math., 16 (2010), 23–30.

  167. On the asymptotic effectiveness of Weil descent attacks, K. Karabina, A. Menezes, C. Pomerance, and I. Shparlinski, J. Math. Crypt., 4 (2010), 175–191.

  168. Fixed points for discrete logarithms, M. Levin, C. Pomerance, and K. Soundararajan, ANTS IX Proceedings, LNCS 6197 (2010), 6–15.

  169. Remarks on the Pólya–Vinogradov inequality, C. Pomerance, Integers (Proceedings of the Integers Conference, October 2009), 11A (2011), Article 19, 11pp.

  170. Fibonacci integers, F. Luca, C. Pomerance, and S. Wagner, J. Number Theory 131 (2011), 440–457.

  171. On composite integers n for which ϕ(n )|n –1, F. Luca and C. Pomerance, Boletin de la Sociedad Matemática Mexicana 17 (2011), 13–21.

  172. Primitive sets with large counting functions, G. Martin and C. Pomerance, Publ. Math. Debrecen, 77 (2011), 521–530.

  173. Multiplicative properties of sets of residues, C. Pomerance and A. Schinzel, Moscow J. Combinatorics and Number Theory, 1 (2011), 52–66.

  174. On numbers n dividing the n th term of a linear recurrence, J. J. Alba González, F. Luca, C. Pomerance, and I. E. Shparlinski, Proc. Edinburgh Math. Soc., 55 (2012), 271–289.

  175. Prime-perfect numbers, P. Pollack and C. Pomerance, Integers (Selfridge memorial issue), 12A (2012), A14, 19 pp.

  176. Infinitude of elliptic Carmichael numbers, A. Ekstrom, C. Pomerance, and D. S. Thakur, J. Australian Math. Soc., 92 (2012), 45–60.

  177. Product-free sets with high density, P. Kurlberg, J. C. Lagarias, and C. Pomerance, Acta Arith., 155 (2012), 163–173.

  178. The average order of elements in the multiplicative group of a finite field, Y. Hu and C. Pomerance, Involve, 5-2 (2012), 229–236.

  179. On sets of integers which are both sum-free and product-free, P. Kurlberg, J. C. Lagarias, and C. Pomerance, Integers (Proceedings of the 2011 Integers Conference), 12B (2012), A4, 9 pp.

  180. On congruences of the form σ(n ) ≡ a (mod n ), A. Anavi, P. Pollack, and C. Pomerance, IJNT, 9 (2012), 115–124.

  181. On a problem of Arnold: the average multiplicative order of a given integer, P. Kurlberg and C. Pomerance, Algebra and Number Theory, 7 (2013), 981–999.

  182. Sets of monotonicity for Euler's totient function, P. Pollack, C. Pomerance, and E. Treviño, Ramanujan J., 30 (2013), 379–398.

  183. On the distribution of some integers related to perfect and amicable numbers, P. Pollack and C. Pomerance, Colloq. Math., 130 (2013), 169–182.

  184. The maximal density of product-free sets in Z/n Z, P. Kurlberg, J. C. Lagarias, and C. Pomerance, Int. Math. Res. Not. IMRN, 2013 (2013) #4, 827–845 (first published online February 14, 2012 doi:10.1093/imrn/rns014).

  185. On balanced subgroups of the multiplicative group, C. Pomerance and D. Ulmer, in Number theory and related fields, in memory of Alf van der Poorten, J. M. Borwein, I. Shparlinski, and W. Zudlin, eds., Springer Proceedings in Mathematics and Statistics 43 (2013), 253–270.

  186. Paul Erdős and the rise of statistical thinking in elementary number theory, P. Pollack and C. Pomerance, pp. 515–523 in Erdős Centennial, L. Lovász, I. Z. Ruzsa, and V. T. Sós, eds., János Bolyai Math. Soc. and Springer-Verlag, Hungary, 2013.

  187. On primes recognizable in deterministic polynomial time, S. Konyagin and C. Pomerance, pp. 159–186 in vol. 1 of The mathematics of Paul Erdős, second edition, R. L. Graham, J. Nesetril, and S. Butler, eds., Springer, New York, 2013. (This article is identical to #111 except for the update found here.)

  188. Variant of a theorem of Erdős on the sum-of-proper-divisors function, C. Pomerance and H.-S. Yang, Math. Comp. 83 (2014), 1903–1913.

  189. On the local behavior of the order of appearance in the Fibonacci sequence, F. Luca and C. Pomerance, IJNT 10 (2014), 915–933; online as DOI: 10.1142/S1793042114500079.

  190. On the range of Carmichael's universal exponent function, F. Luca and C. Pomerance, Acta Arith. 162 (2014), 289–308.

  191. Square values of Euler's function, P. Pollack and C. Pomerance, Bull. London Math. Soc. 46 (2014), 403–414; online as doi: 10.1112/blms/bdt097.

  192. On integers which are the sum of a power of 2 and a polynomial value, F. Luca, C. Gustavo Moreira, and C. Pomerance, Bull. Brazilian Math. Soc. (NS) 45 (2014), 559–574.

  193. The image of Carmichael's λ-function, K. Ford, F. Luca, and C. Pomerance, Algebra & Number Theory 8-8 (2014), 2009–2026. DOI 10.2140/ant.2014.8.2009.

  194. On the counting function of irregular primes, F. Luca, A. Pizarro-Madariaga, and C. Pomerance, Indag. Math. 26 (2015), 147–161, online as http://dx.doi.org/10.1016/j.indag.2014.09.002.

  195. Sierpiński and Carmichael numbers, W. Banks, C. Finch, F. Luca, C. Pomerance, and P. Stănică, Trans. Amer. Math. Soc. 367 (2015), 355–376.

  196. Divisors of the middle binomial coefficient, C. Pomerance, Amer. Math. Monthly 122 (2015), 636–644. (Copyright 2015, Mathematical Association of America. All rights reserved.)

  197. Harmonious pairs, M. Kozek, F. Luca, P. Pollack, and C. Pomerance, IJNT 11 (2015), 1633–1651, online as http://dx.doi.org/10.1142/S1793042115400151

  198. The range of the sum-of-proper-divisors function, F. Luca and C. Pomerance, Acta Arith. 168 (2015), 187–199.

  199. On amicable numbers, C. Pomerance, in Analytic number theory (in honor of Helmut Maier's 60th birthday), M. Rassias and C. Pomerance, eds., Springer, Cham, Switzerland, 2015, pp. 321–327.

  200. On the parity of the number of small divisors of n, K. Ford, F. Luca, C. Pomerance, and J. Shallit, in Analytic number theory (in honor of Helmut Maier's 60th birthday), M. Rassias and C. Pomerance, eds., Springer, Cham, Switzerland, 2015, pp. 93–100.

  201. A note on square totients, T. Freiberg and C. Pomerance, IJNT 11 (2015), 2265–2276, http://www.worldscientific.com/doi/10.1142/S179304211550102X.

  202. Generating random factored Gaussian integers, easily, N. Lebowitz-Lockard and C. Pomerance, Math. Comp. 85 (2016), 503–516.

  203. Some problems of Erdős on the sum-of-divisors function, P. Pollack and C. Pomerance, Trans. Amer. Math. Soc. Ser. B 3 (2016), 1–26,
    http://dx.doi.org/10.1090/btran10.

  204. On integers n for which Xn – 1 has divisors of every degree, C. Pomerance, L. Thompson, and A. Weingartner, Acta Arith. 175 (2016), 225–243.

  205. Numbers divisible by a large shifted prime and large torsion subgroups of CM elliptic curves, N. McNew, P. Pollack, and C. Pomerance, Int. Math. Res. Not. 2017; doi: 10.1093/imrn/rnw173.

  206. Local behavior of the composition of the aliquot and co-totient functions, F. Luca and C. Pomerance, in Analytic number theory, modular forms and q-hypergeometric series — in honor of Krishna Alladi's 60th birthday, G. Andrews and F. Garvan, eds., Springer Proc. Math. Stat. 221, Springer, Cham, 2017, pp. 477–495.

  207. Squarefree smooth numbers and Euclidean prime generators, A. R. Booker and C. Pomerance, Proc. Amer. Math. Soc. 145 (2017), 5035–5042.

  208. Triangles with prime hypotenuse, S. Chow and C. Pomerance, Research in Number Theory 3 (2017), Art. 21, 10 pp., http://rdcu.be/wApe .

  209. The first function and its iterates, C. Pomerance, in Connections in Discrete Mathematics: A Celebration of the Work of Ron Graham, S. Butler, J. Cooper, and G. Hurlbert, eds., Cambridge U. Press, 2018, pp. 125–138.

  210. Improved error bounds for the Fermat primality test on random inputs, J. D. Lichtman and C. Pomerance, Math. Comp. 87 (2018), 2871–2890. https://doi.org/10.1090/mcom/3314 .

  211. Connected components of the graph generated by power maps in prime finite fields, C. Pomerance and I. E. Shparlinski, Integers 18A (special issue in honor of Jeff Shallit), Article 16, 8 pp., 2018.

  212. Explicit estimates for the distribution of numbers free of large prime factors, J. D. Lichtman and C. Pomerance, J. Number Theory 183 (2018), 1–23, https://doi.org/10.1016/j.jnt.2017.08.039 .

  213. Divisor-sum fibers, P. Pollack, C. Pomerance, and L. Thompson, Mathematika 64 (2018), 330–342, https://doi.org/10.1112/S0025579317000535.

  214. The aliquot constant, after Bosma and Kane, C. Pomerance, Quarterly J. Math. 69 (2018), 915–930, https://doi.org/10.1093/qmath/hay005.

  215. Density of singular pairs of integers, R. Nedela and C. Pomerance, Integers 18 (2018), paper A82, 7 pp.

  216. Eigenvalues of the Laplacian on domains with fractal boundaries, P. Pollack and C. Pomerance, in Horizons of Fractal Geometry and Complex Dimensions, San Luis Obispo, June, 2016, R. G. Niemeyer, E. P. J. Pearse, J. A. Rock, and T. Samuel, eds., Contemporary Mathematics Vol. 731, 2019, pp. 267–277. https://doi.org/10.1090/conm/731/14678.

  217. Primality testing with Gaussian periods, H. W. Lenstra, Jr. and C. Pomerance, J. European Math. Soc. 21 (2019), 1229–1269.

  218. The reciprocal sum of the amicable numbers, H. M. Nguyen and C. Pomerance, Math. Comp. 88 (2019), 1503–1526, http://dx.doi.org/10.1090/mcom/3362.

  219. The Erdős conjecture for primitive sets, J. D. Lichtman and C. Pomerance, Proc. Amer. Math. Soc. Ser. B 6 (2019), 1–14, https://doi.org/10.1090/bproc/40.

  220. Primes in prime number races, J. D. Lichtman, G. Martin, and C. Pomerance, Proc. Amer. Math. Soc. 147 (2019), 3743–3757, https://doi.org/10.1090/proc/14569.

  221. Proof of the Sheldon conjecture, C. Pomerance and C. Spicer, Amer. Math. Monthly 126 (2019), 688–698. https://doi.org/10.1080/00029890.2019.1626672.

  222. Counting integers with a smooth totient, W. D. Banks, J. B. Friedlander, C. Pomerance, and I. E. Shparlinski, Quarterly J. Math. 70 (2019), 1371–1386. Also see https://academic.oup.com/qjmath/article/70/4/1371/5560309?guestAccessKey=fea642fd-4661-4933-a7bc-bbfbc19652bc

  223. Progress towards a nonintegrality conjecture, S. Laishram, D. López-Aguayo, C. Pomerance, and T. Thongjunthug, European J. Math. (2019). https://doi.org/10.1007/s40879-019-00353-4.

  224. Symmetric primes revisited, W. Banks, P. Pollack, and C. Pomerance, Integers 19 (2019), #A54, 7pp.

  225. Counting elliptic curves with an isogeny of degree three, M. Pizzo, C. Pomerance, and J. Voight, Proc. Amer. Math. Soc., Ser. B 7 (2020), 28–42. https://doi.org/10.1090/bproc/45.
    (For a missing reference, see https://math.dartmouth.edu/~jvoight/articles/3isog-errata.pdf.)

  226. On the equation ϕ(n) = ϕ(n+1), P. Kinlaw, M. Kobayashi, and C. Pomerance, Acta Arith. 196 (2020), 69–92.

  227. Phi, Primorials, and Poisson, P. Pollack and C. Pomerance, Illinois J. Math. 64 (2020), 319–330.

  228. A generalization of primitive sets and a conjecture of Erdős, T. H. Chan, J. D. Lichtman, and C. Pomerance, Discrete Analysis, 2020:16, 13 pp.

  229. Some thoughts on pseudoprimes, C. Pomerance and S. S. Wagstaff, Jr., Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques 154 No. 46 (2020), 53–72.

  230. Long gaps in sieved sets, K. Ford, S. Konyagin, J. Maynard, C. Pomerance, and T. Tao, J. European Math. Soc. 23 (2021), 667–700. DOI: 10.4171/JEMS/1020 (Published online: 2020-11-15). Corrigendum JEMS 25 (2023), 2483–2485.

  231. Elliptic curves with Galois-stable cyclic subgroups of order 4, C. Pomerance and E. Schaefer, Research in Number Theory 7, Article number: 35 (2021). Available at https://rdcu.be/cj2KY .

  232. A note on Carmichael numbers in residue classes, C. Pomerance, Integers 21A (2021), The Ron Graham Memorial Volume, Article 19, 7 pp.

  233. Algorithms for the multiplication table problem, R. Brent, C. Pomerance, D. Purdum, and J. Webster, Integers 21 (2021), #A92, 19 pp.

  234. On the critical exponent for k-primitive sets, T. H. Chan, J. D. Lichtman, and C. Pomerance, Combinatorica, DOI: 10.1007/s00493-021-4695-2.

  235. Cyclotomic coincidences, C. Pomerance and S. Rubinstein-Salzedo, Exp. Math. 31 (2022), 596–605. .DOI:10.1080/10586458.2019.1660741, published online 19 September, 2019.

  236. On primes and practical numbers, C. Pomerance and A. Weingartner, Ramanujan J. 57 (2022), 981–1000. DOI https://doi.org/10.1007/s11139-020-00354-y, published online Feb. 15, 2021.

  237. Coprime matchings, C. Pomerance, Integers 22 (2022), #A2, 9 pp.

  238. On a nonintegrality conjecture, F. Luca and C. Pomerance, European J. Math. 8 (2022), 634–639.

  239. The man who loved problems: Richard K. Guy, A. Granville and C. Pomerance, Notices of the AMS 69 (2022), 574–585.

  240. Coprime permutations, C. Pomerance, Integers 22 (2022), #83, 20 pp.

  241. The denominators of the Bernoulli numbers, C. Pomerance and S. S. Wagstaff, Jr., Acta Arith. 209 (2023), 1–15.

  242. Permutations with arithmetic constraints, C. Pomerance, in "Number theory in memory of Eduard Wirsing", edited by H. Maier, J. Steuding, and R. Steuding, Springer, Switzerland, 2023, pp. 285–298.

  243. An inequality related to the sieve of Eratosthenes, K. (S.) Fan and C. Pomerance, J. Number Theory 254 (2024), 169–183.

  244. Shifted-prime divisors, K. (S.) Fan and C. Pomerance, preprint, January 18, 2024. (Current version from May 10, 2024.) To appear in a Springer volume dedicated to Helmut Maier on his 70th birthday and edited by J. Friedlander, C. Pomerance, and M. Rassias.

  245. Cyclotomic primes, C. Pomerance, J. Number Theory 276 (2025), 198–208. (Printed version available until July 1, 2025: https://authors.elsevier.com/a/1l4o6,WUBIsSg . Also available at libraries and perhaps in a few years by Elsevier.)

  246. Counting solvable S-unit equations and linear recurrence sequences with zeros, A. Ostafe, C. Pomerance, and I. Shparlinski, submitted for publication, March 12, 2025.

  247. Patterns for cyclic numbers, C. Pomerance, submitted for publication, March 12, 2025.

  248. Correction to: On Robin's inequality, F. Luca, C. Pomerance, and P. Solé, Integers, to appear.

  249. A generalization of primitive roots, S. Li and C. Pomerance, submitted for publication, April 7, 2025. (There is some overlap between this survey article and #131.)

  250. Fermat pseudoprimes, S. Li and C. Pomerance, submitted for publication, April 11, 2025.

    Last modified May, 2025.