Carl Pomerance

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All published works

Action	Title	Year	Authors
+ PDF Chat	Cyclotomic primes	2024	Carl Pomerance
+	Shifted-prime divisors	2024	Steve Fan Carl Pomerance
+	An inequality related to the sieve of Eratosthenes	2023	Kai Fan Carl Pomerance
+	An inequality related to the sieve of Eratosthenes	2023	Steve Fan Carl Pomerance
+	Permutations with Arithmetic Constraints	2023	Carl Pomerance
+	On a problem of Evelyn--Linfoot and Page in additive number theory	2022	Carl Pomerance D. Suryanarayana
+ PDF	A note on Carmichael numbers in residue classes	2022	Carl Pomerance
+	The denominators of the Bernoulli numbers	2022	Carl Pomerance Samuel S. Wagstaff
+	Permutations with arithmetic constraints	2022	Carl Pomerance
+	Coprime permutations	2022	Carl Pomerance
+ PDF Chat	On the Critical Exponent for k-Primitive Sets	2021	Tsz Ho Chan Jared Duker Lichtman Carl Pomerance
+	Coprime matchings.	2021	Carl Pomerance
+ PDF Chat	On a nonintegrality conjecture	2021	Florian Luca Carl Pomerance
+	On a nonintegrality conjecture	2021	Florian Luca Carl Pomerance
+ PDF Chat	Elliptic curves with Galois-stable cyclic subgroups of order 4	2021	Carl Pomerance Edward F. Schaefer
+	Some thoughts on pseudoprimes	2021	Carl Pomerance Samuel S. Wagstaff
+ PDF Chat	On primes and practical numbers	2021	Carl Pomerance Andreas Weingartner
+	On a nonintegrality conjecture	2021	Florian Luca Carl Pomerance
+	The denominators of the Bernoulli numbers	2021	Carl Pomerance Samuel S. Wagstaff
+	Some thoughts on pseudoprimes	2021	Carl Pomerance Samuel S. Wagstaff
+	A note on Carmichael numbers in residue classes	2021	Carl Pomerance
+	Coprime matchings	2021	Carl Pomerance
+	On the critical exponent for $k$-primitive sets	2020	Tsz Ho Chan Jared Duker Lichtman Carl Pomerance
+ PDF Chat	Long gaps in sieved sets	2020	Kevin Ford Sergey Konyagin James Maynard Carl Pomerance Terence Tao
+ PDF	A generalization of primitive sets and a conjecture of Erdős	2020	Tsz Ho Chan Jared Duker Lichtman Carl Pomerance
+	On primes and practical numbers	2020	Carl Pomerance Andreas Weingartner
+ PDF Chat	Phi, primorials, and Poisson	2020	Paul Pollack Carl Pomerance
+	Elliptic curves with Galois-stable cyclic subgroups of order 4	2020	Carl Pomerance Edward F. Schaefer
+ PDF	Counting elliptic curves with an isogeny of degree three	2020	Maggie Pizzo Carl Pomerance John Voight
+	On the equation $\varphi (n)=\varphi (n+1)$	2020	Paul Kinlaw Mitsuo KOBAYASHI Carl Pomerance
+	On primes and practical numbers	2020	Carl Pomerance Andreas Weingartner
+	Elliptic curves with Galois-stable cyclic subgroups of order 4	2020	Carl Pomerance Edward F. Schaefer
+	Residue classes free of values of Euler's function	2020	Kevin R. Ford Sergeĭ Konyagin Carl Pomerance
+ PDF Chat	Cyclotomic Coincidences	2019	Carl Pomerance Simon Rubinstein‐Salzedo
+	Proof of the Sheldon Conjecture	2019	Carl Pomerance Chris Spicer
+ PDF Chat	COUNTING INTEGERS WITH A SMOOTH TOTIENT	2019	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski
+	Algorithms for the Multiplication Table Problem	2019	Richard P. Brent Carl Pomerance David Purdum Jonathan Webster
+	Symmetric primes revisited	2019	William D. Banks Paul Pollack Carl Pomerance
+ PDF Chat	Progress towards a nonintegrality conjecture	2019	Shanta Laishram Daniel López-Aguayo Carl Pomerance Thotsaphon Thongjunthug
+	Counting elliptic curves with an isogeny of degree three	2019	Maggie Pizzo Carl Pomerance John Voight
+ PDF	The Erdős conjecture for primitive sets	2019	Jared Duker Lichtman Carl Pomerance
+	Progress towards a nonintegrality conjecture	2019	Shanta Laishram Daniel López-Aguayo Carl Pomerance Thotsaphon Thongjunthug
+	Primes in prime number races	2019	Jared Duker Lichtman Greg Martin Carl Pomerance
+ PDF	Primality testing with Gaussian periods	2019	Hendrik W. Lenstra Carl Pomerance
+ PDF	Eigenvalues of the Laplacian on domains with fractal boundary	2019	Paul Pollack Carl Pomerance
+	Symmetric primes revisited	2019	William D. Banks Paul Pollack Carl Pomerance
+	Algorithms for the Multiplication Table Problem	2019	Richard P. Brent Carl Pomerance David Purdum Jonathan Webster
+	Counting elliptic curves with an isogeny of degree three	2019	Maggie Pizzo Carl Pomerance John Voight
+	Progress towards a nonintegrality conjecture	2019	Shanta Laishram Daniel López-Aguayo Carl Pomerance Thotsaphon Thongjunthug
+	Cyclotomic Coincidences	2019	Carl Pomerance Simon Rubinstein‐Salzedo
+	The First Function and Its Iterates	2018	Carl Pomerance
+ PDF	The reciprocal sum of the amicable numbers	2018	Hanh Nguyen Carl Pomerance
+	The aliquot constant, after Bosma and Kane	2018	Carl Pomerance
+	Counting integers with a smooth totient	2018	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski
+	Density of singular pairs of integers	2018	Roman Nedela Carl Pomerance
+ PDF	DIVISOR‐SUM FIBERS	2018	Paul Pollack Carl Pomerance Lola Thompson
+	Explicit estimates for the distribution of numbers free of large prime factors	2017	Jared Duker Lichtman Carl Pomerance
+ PDF Chat	Improved error bounds for the Fermat primality test on random inputs	2017	Jared Duker Lichtman Carl Pomerance
+ PDF	Triangles with prime hypotenuse	2017	Sam Chow Carl Pomerance
+	Connected components of the graph generated by power maps in prime finite fields	2017	Carl Pomerance Igor E. Shparlinski
+	Local Behavior of the Composition of the Aliquot and Co-Totient Functions	2017	Florian Luca Carl Pomerance
+	Triangles with prime hypotenuse	2017	Sam Chow Carl Pomerance
+	Squarefree smooth numbers and Euclidean prime generators	2016	Andrew R. Booker Carl Pomerance
+	Numbers Divisible by a Large Shifted Prime and Large Torsion Subgroups of CM Elliptic Curves	2016	Nathan McNew Paul Pollack Carl Pomerance
+	Squarefree smooth numbers and Euclidean prime generators	2016	Andrew R. Booker Carl Pomerance
+	Corrigendum: `On the average number of divisors of the Euler function'	2016	Florian Luca Carl Pomerance
+ PDF	Some problems of Erdős on the sum-of-divisors function	2016	Paul Pollack Carl Pomerance
+ PDF Chat	On integers $n$ for which $X^n-1$ has a divisor of every degree	2016	Carl Pomerance Lola Thompson Andreas Weingartner
+	Squarefree smooth numbers and Euclidean prime generators	2016	Andrew R. Booker Carl Pomerance
+	Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday	2015	Carl Pomerance Michael Th. Rassias
+	On integers $n$ for which $X^n-1$ has a divisor of every degree	2015	Carl Pomerance Lola Thompson Andreas Weingartner
+ PDF Chat	A note on square totients	2015	Tristan Freiberg Carl Pomerance
+ PDF	Generating random factored Gaussian integers, easily	2015	Noah Lebowitz-Lockard Carl Pomerance
+	Harmonious pairs	2015	Mark Kozek Florian Luca Paul Pollack Carl Pomerance
+	On Amicable Numbers	2015	Carl Pomerance
+	The range of the sum-of-proper-divisors function	2015	Florian Luca Carl Pomerance
+	On the Parity of the Number of Small Divisors of n	2015	Kevin Ford Florian Luca Carl Pomerance Jeffrey Shallit
+	On integers $n$ for which $X^n-1$ has a divisor of every degree	2015	Carl Pomerance Lola Thompson Andreas Weingartner
+ PDF	The image of Carmichael’s<i>λ</i>-function	2014	Kevin Ford Florian Luca Carl Pomerance
+	Sierpiński and Carmichael numbers	2014	William D. Banks Carrie E. Finch Florian Luca Carl Pomerance Pantelimon Stănică
+	On the counting function of irregular primes	2014	Florian Luca Amalia Pizarro-Madariaga Carl Pomerance
+	On integers which are the sum of a power of 2 and a polynomial value	2014	Florian Luca Carlos Gustavo Moreira Carl Pomerance
+	Square values of Euler's function	2014	Paul Pollack Carl Pomerance
+ PDF	On the range of Carmichael's universal-exponent function	2014	Florian Luca Carl Pomerance
+	Avoiding Geometric Progressions in the Integers	2014	Nathan McNew Carl Pomerance
+	Algebra & Number Theory	2014	Pär Kurlberg Carl Pomerance
+	On the local behavior of the order of appearance in the Fibonacci sequence	2013	Florian Luca Carl Pomerance
+	Variant of a theorem of Erdős on the sum-of-proper-divisors function	2013	Carl Pomerance Hee-Sung Yang
+ PDF	On a problem of Arnold: The average multiplicative order of a given integer	2013	Pär Kurlberg Carl Pomerance
+	Combinatorial Number Theory	2013	Carl Pomerance Andràs Sárközy
+ PDF Chat	On Balanced Subgroups of the Multiplicative Group	2013	Carl Pomerance Douglas Ulmer
+	On Primes Recognizable in Deterministic Polynomial Time	2013	Sergeĭ Konyagin Carl Pomerance
+ PDF	On the distribution of some integers related to perfect and amicable numbers	2013	Paul Pollack Carl Pomerance
+	Paul Erdős and the Rise of Statistical Thinking in Elementary Number Theory	2013	Paul Pollack Carl Pomerance
+ PDF	The average order of elements in the multiplicative group of a finite field	2012	Yilan Hu Carl Pomerance
+	Sets of monotonicity for Euler’s totient function	2012	Paul Pollack Carl Pomerance Enrique Treviño
+	ON CONGRUENCES OF THE FORM σ(n) ≡ a (<font>mod</font>n)	2012	ARIA ANAVI Paul Pollack Carl Pomerance
+	Prime Numbers: A Computational Perspective	2012	Richard E. Crandall Carl Pomerance
+	On balanced subgroups of the multiplicative group	2012	Carl Pomerance Douglas Ulmer
+ PDF	Irreducible radical extensions and Euler-function chains	2012	Florian Luca Carl Pomerance
+ PDF	On numbers <i>n</i> dividing the <i>n</i>th term of a linear recurrence	2012	Juan José Alba González Florian Luca Carl Pomerance Igor E. Shparlinski
+ PDF Chat	The Maximal Density of Product-Free Sets in ℤ/nℤ	2012	Pär Kurlberg Jeffrey C. Lagarias Carl Pomerance
+ PDF	INFINITUDE OF ELLIPTIC CARMICHAEL NUMBERS	2012	Aaron Todd Ekstrom Carl Pomerance Dinesh S. Thakur
+	On sets of integers which are both sum-free and product-free	2012	Pär Kurlberg Jeffrey C. Lagarias Carl Pomerance
+ PDF	Product-free sets with high density	2012	Pär Kurlberg Jeffrey C. Lagarias Carl Pomerance
+	Prime-Perfect Numbers	2012	Paul Pollack Carl Pomerance
+ PDF	Acknowledgment of priority: ``On some problems of Mąkowski–Schinzel and Erdős concerning the arithmetical functions φ and σ'' (Colloq. Math. 92 (2002), 111–130)	2012	Florian Luca Carl Pomerance
+	On Sets of Integers Which Are Both Sum-Free and Product-Free	2012	Pär Kurlberg Jeffrey C. Lagarias Carl Pomerance
+	On balanced subgroups of the multiplicative group	2012	Carl Pomerance Douglas Ulmer
+	On sets of integers which are both sum-free and product-free	2012	Pär Kurlberg Jeffrey C. Lagarias Carl Pomerance
+	Primitive sets with large counting functions	2011	Greg Martin Carl Pomerance
+	On a problem of Arnold: the average multiplicative order of a given integer	2011	Pär Kurlberg Carl Pomerance
+ PDF	Remarks on the Pólya–Vinogradov Inequality	2011	Carl Pomerance
+	On a problem of Arnold: the average multiplicative order of a given integer	2011	Pär Kurlberg Carl Pomerance
+	IV.3 Computational Number Theory	2010	Carl Pomerance
+	Fibonacci integers	2010	Florian Luca Carl Pomerance Stephan Wagner
+	On numbers $n$ dividing the $n$th term of a linear recurrence	2010	Juan José Alba González Florian Luca Carl Pomerance Igor E. Shparlinski
+	Primitive sets with large counting functions	2010	Greg Martin Carl Pomerance
+ PDF	Error estimates for the Davenport-Heilbronn theorems	2010	Karim Belabas Manjul Bhargava Carl Pomerance
+ PDF	ON CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS	2010	William D. Banks Carl Pomerance
+ PDF Chat	Common values of the arithmetic functions <i>ϕ</i> and <i>σ</i>	2010	Kevin Ford Florian Luca Carl Pomerance
+	Fixed Points for Discrete Logarithms	2010	Mariana Levin Carl Pomerance K. Soundararajan
+	On the radical of a perfect number	2010	Florian Luca Carl Pomerance
+ PDF	Rank Statistics for a Family of Elliptic Curves over a Function Field	2010	Carl Pomerance Igor E. Shparlinski
+	On numbers $n$ dividing the $n$th term of a linear recurrence	2010	Juan José Alba González Florian Luca Carl Pomerance Igor E. Shparlinski
+	Primitive sets with large counting functions	2010	Greg S. Martin Carl Pomerance
+ PDF	On the Distribution of Pseudopowers	2009	Sergeĭ Konyagin Carl Pomerance Igor E. Shparlinski
+	The Artin–Carmichael Primitive Root Problem on Average	2009	Shuguang Li Carl Pomerance
+ PDF	A REMARK ON GIUGA’S CONJECTURE AND LEHMER’S TOTIENT PROBLEM	2009	William D. Banks C. Wesley Nevans Carl Pomerance
+	Combinatorial Number Theory	2009	Bruce Landman Melvyn B. Nathanson Jaroslav Nešetřil Richard J. Nowakowski Carl Pomerance Aaron Robertson
+ PDF Chat	On Pseudosquares and Pseudopowers	2009	Carl Pomerance Igor E. Shparlinski
+ PDF	On the Range of the Iterated Euler Function	2009	Florian Luca Carl Pomerance
+ PDF	On the distribution of sociable numbers	2009	Mitsuo KOBAYASHI Paul Pollack Carl Pomerance
+ PDF	On the smallest pseudopower	2009	Jean Bourgain Sergeĭ Konyagin Carl Pomerance Igor E. Shparlinski
+	Rank statistics for a family of elliptic curves over a function field	2009	Carl Pomerance Igor E. Shparlinski
+	On Giuga numbers	2009	Florian Luca Carl Pomerance Igor E. Shparlinski
+	On pseudosquares and pseudopowers	2009	Carl Pomerance Igor E. Shparlinski
+	On composite integers n for which '(n) j n 1	2009	Florian Luca Carl Pomerance
+	On the proportion of numbers coprime to a given integer	2008	Paul Erdös Florian Luca Carl Pomerance
+	Smooth numbers and the quadratic sieve	2008	Carl Pomerance
+	SETS WITH PRESCRIBED ARITHMETIC DENSITIES	2008	Florian Luca Carl Pomerance
+	ON THE RANGE OF THE ITERATED EULER FUNCTION	2008	Florian Luca Carl Pomerance
+	Combinatorial Number Theory	2007	Bruce Landman Melvyn B. Nathanson Jaroslav Nesetril Richard J. Nowakowski Carl Pomerance
+ PDF	Maximal height of divisors of $x\sp n-1$	2007	Carl Pomerance Nathan C. Ryan
+	The Quadratic Sieve Factoring Algorithm	2007	Carl Pomerance
+	On the average number of divisors of the Euler function	2007	Florian Luca Carl Pomerance
+	On Pseudosquares and Pseudopowers	2007	Carl Pomerance Igor E. Shparlinski
+ PDF	Irreducible Radical Extensions and Euler-function Chains	2006	Florian Luca Carl Pomerance
+	Sieving by large integers and covering systems of congruences	2006	Michael Filaseta Kevin Ford Sergeĭ Konyagin Carl Pomerance Gang Yu
+ PDF	Finding the group structure of elliptic curves over finite fields	2005	John Friedlander Carl Pomerance Igor E. Shparlinski
+	On the Distribution in Residue Classes of Integers with a Fixed Sum of Digits	2005	Christian Mauduit Carl Pomerance Andràs Sárközy
+ PDF	Products of Ratios of Consecutive Integers	2005	Régis de la Bretèche Carl Pomerance Gérald Tenenbaum
+ PDF	The iterated Carmichael λ-function and the number of cycles of the power generator	2005	Greg Martin Carl Pomerance
+	Corrigendum to: On the problem of uniqueness for the maximum Stirling number(s) of the second kind.	2005	E. Rodney Canfield Carl Pomerance
+	Sieving by large integers and covering systems of congruences	2005	Michael Filaseta Kevin Ford Sergeĭ Konyagin Carl Pomerance Gang Yu
+ PDF	On the periods of the linear congruential and power generators	2005	Pär Kurlberg Carl Pomerance
+ PDF	On products of ratios of consecutive integers	2005	Régis de la Bretèche Carl Pomerance Gérald Tenenbaum
+ PDF	On the largest prime factor of a Mersenne number	2004	Leo Murata Carl Pomerance
+ PDF	Multiplicative structure of values of the Euler function	2004	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski
+ PDF	Heuristics for class numbers of prime-power real cyclotomic fields	2004	Joe Buhler Carl Pomerance Leanne Robertson
+ PDF	On the binary expansions of algebraic numbers	2004	David H. Bailey Jonathan M. Borwein Richard E. Crandall Carl Pomerance
+	On the binary expansions of algebraic numbers	2003	David H. Bailey Jonathan M. Borwein Richard E. Crandall Carl Pomerance
+	On the binary expansions of algebraic numbers	2003	David H. Bailey Jonathan M. Borwein Richard E. Crandall Carl Pomerance
+	On generalizing Artins conjecture on primitive roots to composite moduli	2003	Shuguang Li Carl Pomerance
+	Timed Fair Exchange of Standard Signatures	2003	Juan A. Garay Carl Pomerance
+	Primitive roots : a survey (New Aspects of Analytic Number Theory)	2002	Shuguang Li Carl Pomerance
+ PDF	Corrigendum to ``Period of the power generator and small values of Carmichael's function''	2002	John Friedlander Carl Pomerance Igor E. Shparlinski
+ PDF	On the Problem of Uniqueness for the Maximum Stirling Number(s) of the Second Kind	2002	E. Rodney Canfield Carl Pomerance
+	Primitive Roots: A Survey	2002	LI Shu-guang Carl Pomerance
+ PDF	Smooth Orders and Cryptographic Applications	2002	Carl Pomerance Igor E. Shparlinski
+	None	2002	Carl Pomerance
+ PDF	A Hyperelliptic Smoothness Test, II	2002	H. W. Lenstra Jonathan Pila Carl Pomerance
+ PDF	On some problems of Mąkowski–Schinzel and Erdős concerning the arithmetical functions φ and σ	2002	Florian Luca Carl Pomerance
+ PDF	Two contradictory conjectures concerning Carmichael numbers	2001	Andrew Granville Carl Pomerance
+	Elliptic Curve Arithmetic	2001	Richard E. Crandall Carl Pomerance
+	ON THE PROBLEM OF UNIQUENESS FOR THE MAXIMUM STIRLING NUMBER(S) OF THE SECOND KIND	2001	E. Rodney Canfield Carl Pomerance
+	Fast Algorithms for Large-Integer Arithmetic	2001	Richard E. Crandall Carl Pomerance
+	Recognizing Primes and Composites	2001	Richard E. Crandall Carl Pomerance
+	Primes!	2001	Richard S. Crandall Carl Pomerance
+	Prime Numbers	2001	Richard S. Crandall Carl Pomerance
+	Primality Proving	2001	Richard S. Crandall Carl Pomerance
+	Number-Theoretical Tools	2001	Richard E. Crandall Carl Pomerance
+ PDF Chat	Residue classes free of values of Euler’s function	1999	Kevin Ford Sergeĭ Konyagin Carl Pomerance
+	On the solutions to φ(n) = φ(n + k)	1999	S. W. Graham Jeffrey J. Holt Carl Pomerance
+	Number Theory	1999	Jon Grantham Carl Pomerance Bart Goddard Jeff Shallit
+	On the distribution of champs	1999	Aleksandar Ivić Carl Pomerance
+	Euler’s Function in Residue Classes	1998	Thomas P. Dence Carl Pomerance
+	None	1998	Thomas P. Dence Carl Pomerance
+ PDF	A search for Wieferich and Wilson primes	1997	Richard E. Crandall Karl Dilcher Carl Pomerance
+	None	1997	P. Erdős Carl Pomerance Andràs Sárközy
+	On Primes Recognizable in Deterministic Polynomial Time	1997	Sergeĭ Konyagin Carl Pomerance
+	Symmetric and Asymmetric Primes	1996	Peter Fletcher William F. Lindgren Carl Pomerance
+	Counterexamples to the modified Weyl–Berry conjecture on fractal drums	1996	Michel L. Lapidus Carl Pomerance
+	On the number of divisors of n!	1996	Paul Erdös S. W. Graham Aleksandar Ivić Carl Pomerance
+	On a Conjecture of Crandall Concerning the qx + 1 Problem	1995	Zachary Franco Carl Pomerance
+ PDF	On a conjecture of Crandall concerning the 𝑞𝑥+1 problem	1995	Zachary Franco Carl Pomerance
+	Combinatorial Number Theory	1995	Carl Pomerance Andràs Sárközy
+	The Role of Smooth Numbers in Number Theoretic Algorithms	1995	Carl Pomerance
+ PDF	On a Conjecture of R.L. Graham	1994	Fred Yuanyou Cheng Carl Pomerance
+	There are Infinitely Many Carmichael Numbers	1994	W. R. Alford Andrew Granville Carl Pomerance
+	On the difficulty of finding reliable witnesses	1994	W. R. Alford Andrew Granville Carl Pomerance
+ PDF	The number field sieve	1994	Carl Pomerance
+ PDF	A hyperelliptic smoothness test. I	1993	H. W. Lenstra Jonathan Pila Carl Pomerance
+	On Elements of Sumsets with Many Prime Factors	1993	P. Erdős Carl Pomerance Andràs Sárközy C. L. Stewart
+	Corrigendum: The Distribution of Lucas and Elliptic Pseudoprimes	1993	Daniel M. Gordon Carl Pomerance
+ PDF	Corrigendum: “The distribution of Lucas and elliptic pseudoprimes” [Math. Comp. 57 (1991), no. 196, 825–838; MR1094951 (92h:11081)]	1993	Daniel M. Gordon Carl Pomerance
+ PDF	An upper bound in Goldbach’s problem	1993	Jean-Marc Deshouillérs Andrew Granville Władysław Narkiewicz Carl Pomerance
+ PDF	Average case error estimates for the strong probable prime test	1993	Ivan Damgård Peter Landrock Carl Pomerance
+	Factoring integers with the number field sieve	1993	Joe Buhler H. W. Lenstra Carl Pomerance
+ PDF	The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums	1993	Michel L. Lapidus Carl Pomerance
+ PDF	A Rigorous Time Bound for Factoring Integers	1992	H. W. Lenstra Carl Pomerance
+ PDF	The Distribution of Smooth Numbers in Arithmetic Progressions	1992	Antal Balog Carl Pomerance
+	Grandes déviations pour certaines fonctions arithmétiques	1992	Michel Balazard Judith Nicolas Carl Pomerance Gérald Tenenbaum
+ PDF	The distribution of smooth numbers in arithmetic progressions	1992	Antal Balog Carl Pomerance
+ PDF	The Distribution of Lucas and Elliptic Pseudoprimes	1991	Daniel M. Gordon Carl Pomerance
+ PDF	Carmichael's lambda function	1991	P. Erdős Carl Pomerance Eric Schmutz
+ PDF	The distribution of Lucas and elliptic pseudoprimes	1991	Daniel M. Gordon Carl Pomerance
+ PDF	On prime divisors of Mersenne numbers	1991	P. Erdős Péter Kiss Carl Pomerance
+ PDF	Unusually Large Gaps Between Consecutive Primes	1990	Helmut Maier Carl Pomerance
+	On the Least Prime in Certain Arithmetic Progressions	1990	Andrew Granville Carl Pomerance
+	On the Normal Behavior of the Iterates Of some Arithmetic Functions	1990	Paul Erdös Andew Granvilie Carl Pomerance Claudia Spiro
+ PDF	Unusually large gaps between consecutive primes	1990	Helmut Maier Carl Pomerance
+	Unusually large gaps between consecutive primes	1989	Helmut Maier Carl Pomerance
+	<i>The Book of Prime Number Records</i>. By Paulo Ribenboim	1989	Carl Pomerance
+ PDF	On the composition of the arithmetic functions σ and φ	1989	Carl Pomerance
+ PDF	The probability that a random probable prime is composite	1989	Su Hee Kim Carl Pomerance
+ PDF	On divisors of sums of integers. III	1988	Carl Pomerance Andràs Sárközy C. L. Stewart
+ PDF	On homogeneous multiplicative hybrid problems in number theory	1988	Carl Pomerance Andràs Sárközy
+ PDF	Book Review: Prime numbers and computer methods for factorization	1988	Carl Pomerance
+ PDF	On the number of distinct values of Euler's φ-function	1988	Helmut Maier Carl Pomerance
+ PDF	The generation of random numbers that are probably prime	1988	Pierre Beauchemin Gilles Brassard Claude Crépeau Claude Goutier Carl Pomerance
+	On Locally Repeated Values of Certain Arithmetic Functions. III	1987	Paul Erdös Carl Pomerance Andràs Sárközy
+ PDF	The smallestn-uniform hypergraph with positive discrepancy	1987	Noga Alon Daniel J. Kleitman Carl Pomerance Michael Saks Paul Seymour
+ PDF	On locally repeated values of certain arithmetic functions. II	1987	Paul Erdös Carl Pomerance Andràs Sárközy
+ PDF	On the average number of groups of square-free order	1987	Carl Pomerance
+ PDF	On the Average Number of Groups of Square-Free Order	1987	Carl Pomerance
+ PDF	Very short primality proofs	1987	Carl Pomerance
+ PDF	On locally repeated values of certain arithmetic functions. III	1987	P. Erdős Carl Pomerance Andràs Sárközy
+ PDF	Very Short Primality Proofs	1987	Carl Pomerance
+	On the number of false witnesses for a composite number	1987	Paul Erdös Carl Pomerance
+ PDF	On primitive divisors of Mersenne numbers	1986	Carl Pomerance
+	On the Number of False Witnesses for a Composite Number	1986	Paul Erdös Carl Pomerance
+ PDF	On the number of false witnesses for a composite number	1986	Paul Erdös Carl Pomerance
+ PDF	On the distribution of the values of Euler's function	1986	Carl Pomerance
+	On locally repeated values of certain arithmetic functions, I	1985	Paul Erdös Andràs Sárközy Carl Pomerance
+	Multiplicative Relations for Sums of Initial <i>k</i>th Powers	1985	David E. Penney Carl Pomerance
+	Multiplicative Relations for Sums of Initial kth Powers	1985	David E. Penney Carl Pomerance
+ PDF	On the normal number of prime factors of $\phi(n)$	1985	Paul Erdös Carl Pomerance
+	On the distribution of round numbers	1985	Carl Pomerance
+	The Quadratic Sieve Algorithm	1985	Carl Pomerance
+	On a problem of Oppenheim concerning “factorisatio numerorum”	1983	E. Rodney Canfield Paul Erdös Carl Pomerance
+	On Distinguishing Prime Numbers from Composite Numbers	1983	Leonard M. Adleman Carl Pomerance Robert Rumely
+	The Search for Prime Numbers	1982	Carl Pomerance
+ PDF	A new lower bound for the pseudoprime counting function	1982	Carl Pomerance
+ PDF	On the Distribution of Pseudoprimes	1981	Carl Pomerance
+	Sets on which an entire function is determined by its range	1981	Harold G. Diamond Carl Pomerance Lee A. Rubel
+	On the distribution of amicable numbers. II.	1981	Carl Pomerance
+ PDF	On the distribution of pseudoprimes	1981	Carl Pomerance
+	The arithmetic mean of the divisors of an integer	1981	Paul T. Bateman Paul Erdös Carl Pomerance E. G. Straus
+	The Pseudoprimes to 25 ⋅10 9	1980	Carl Pomerance J. L. Selfridge Samuel S. Wagstaff
+	Proof of D. J. Newman's coprime mapping conjecture	1980	Carl Pomerance J. L. Selfridge
+	Popular values of Euler's function	1980	Carl Pomerance
+	A note on the least prime in an arithmetic progression	1980	Carl Pomerance
+	Collinear subsets of lattice point sequences—An analog of Szemerédi's theorem	1980	Carl Pomerance
+ PDF	The pseudoprimes to 25⋅10⁹	1980	Carl Pomerance J. L. Selfridge Samuel S. Wagstaff
+	Nearly parallel vectors	1979	Harold G. Diamond Carl Pomerance
+ PDF	The prime number graph	1979	Carl Pomerance
+ PDF	The Prime Number Graph	1979	Carl Pomerance
+	On a class of relatively prime sequences	1978	P. Erdős David E. Penney Carl Pomerance
+ PDF	On the largest prime factors ofn andn + 1	1978	P. Erdős Carl Pomerance
+	On the largest prime factors ofn andn + 1	1978	Paul Erdös Carl Pomerance
+	Multiply perfect numbers, mersenne primes, and effective computability	1977	Carl Pomerance
+ PDF	On composite<i>n</i>for which<i>φ</i>(<i>n</i>)<i>∣</i><i>n</i>− 1. II	1977	Carl Pomerance
+	On a tiling problem of R.B. Eggleton	1977	Carl Pomerance
+ PDF	On composite n for which φ(n) \| n -1	1976	Carl Pomerance
+ PDF	The Second Largest Prime Factor of an Odd Perfect Number	1975	Carl Pomerance
+ PDF	Three Elliptic Curves with Rank at Least Seven	1975	David E. Penney Carl Pomerance
+ PDF	On multiply perfect numbers with a special property	1975	Carl Pomerance
+ PDF	Some new results on odd perfect numbers	1975	G. G. Dandapat John Hunsucker Carl Pomerance
+ PDF	On the congruences $σ(n) ≡ a (mod n)$ and $n ≡ a (mod φ(n))$	1975	Carl Pomerance
+ PDF	The second largest prime factor of an odd perfect number	1975	Carl Pomerance
+ PDF	Three elliptic curves with rank at least seven	1975	David E. Penney Carl Pomerance
+ PDF	A Search for Elliptic Curves With Large Rank	1974	David E. Penney Carl Pomerance
+	On Carmichael's Conjecture	1974	Carl Pomerance
+ PDF	Odd perfect numbers are divisible by at least seven distinct primes	1974	Carl Pomerance
+ PDF	A search for elliptic curves with large rank	1974	David E. Penney Carl Pomerance
+	On Carmichael’s conjecture	1974	Carl Pomerance

Common Coauthors

Coauthor	Papers Together
Florian Luca	31
Igor E. Shparlinski	18
Paul Pollack	15
Paul Erdös	13
Andràs Sárközy	11
Pär Kurlberg	10
Richard E. Crandall	9
William D. Banks	8
Sergeĭ Konyagin	8
Kevin Ford	7
Jared Duker Lichtman	7
P. Erdős	7
David E. Penney	7
Samuel S. Wagstaff	6
Andreas Weingartner	6
John Friedlander	5
Jeffrey C. Lagarias	5
Andrew Granville	5
E. Rodney Canfield	4
Daniel M. Gordon	4
Lola Thompson	4
H. W. Lenstra	4
Greg Martin	4
Shanta Laishram	3
Tsz Ho Chan	3
David H. Bailey	3
Maggie Pizzo	3
Thotsaphon Thongjunthug	3
John Voight	3
Edward F. Schaefer	3
Helmut Maier	3
Andrew R. Booker	3
Richard S. Crandall	3
Gérald Tenenbaum	3
Douglas Ulmer	3
Daniel López-Aguayo	3
Juan José Alba González	3
Jonathan M. Borwein	3
J. L. Selfridge	3
Nathan McNew	2
Richard J. Nowakowski	2
Richard P. Brent	2
Zachary Franco	2
Simon Rubinstein‐Salzedo	2
Melvyn B. Nathanson	2
W. R. Alford	2
Michel L. Lapidus	2
Sam Chow	2
Jonathan Pila	2
Michael Filaseta	2

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF	Approximate formulas for some functions of prime numbers	1962	J. Barkley Rosser Lowell Schoenfeld	29
+	On The Number of Positive Integers ≤ x and Free of Prime Factors > y	1951	N.G. de Bruijn	25
+	There are Infinitely Many Carmichael Numbers	1994	W. R. Alford Andrew Granville Carl Pomerance	23
+	ON THE NORMAL NUMBER OF PRIME FACTORS OF <i>p</i>-1 AND SOME RELATED PROBLEMS CONCERNING EULER'S ø-FUNCTION	1935	P. Erdős	21
+	On a problem of Oppenheim concerning “factorisatio numerorum”	1983	E. Rodney Canfield Paul Erdös Carl Pomerance	21
+	Multiplicative Number Theory	1980	H. Davenport	20
+	On the distribution of amicable numbers. II.	1981	Carl Pomerance	20
+ PDF	Shifted primes without large prime factors	1998	Roger C. Baker G. Harman	18
+ PDF	Carmichael's lambda function	1991	P. Erdős Carl Pomerance Eric Schmutz	18
+	An Introduction to the Theory of Numbers. By G. H. Hardy and E. M. Wright. 2nd edition. Pp. xvi, 407 25s. 1945. (Oxford)	1946	T. A. A. B.	17
+	Introduction to Analytic and Probabilistic Number Theory	2015	Gérald Tenenbaum	15
+	Popular values of Euler's function	1980	Carl Pomerance	15
+ PDF	On the distribution of pseudoprimes	1981	Carl Pomerance	14
+	On Artin's conjecture.	1967	C. Hooley	14
+ PDF	An introduction to the theory of numbers	1960	G. H. Hardy	14
+	On pseudoprimes and Carmichael numbers	2022	P. Erdős	13
+ PDF	Unsolved Problems in Number Theory	1994	Richard K. Guy	12
+	On the Normal Behavior of the Iterates Of some Arithmetic Functions	1990	Paul Erdös Andew Granvilie Carl Pomerance Claudia Spiro	12
+	Prime Numbers: A Computational Perspective	2012	Richard E. Crandall Carl Pomerance	12
+ PDF	On the number of restricted prime factors of an integer. I	1976	Karl K. Norton	12
+ PDF	The distribution of integers with a divisor in a given interval	2008	Kevin Ford	11
+ PDF	Factoring Integers with Elliptic Curves	1987	H. W. Lenstra	11
+	None	1998	Kevin Ford	11
+	On generalizing Artins conjecture on primitive roots to composite moduli	2003	Shuguang Li Carl Pomerance	11
+ PDF	The pseudoprimes to 25⋅10⁹	1980	Carl Pomerance J. L. Selfridge Samuel S. Wagstaff	10
+ PDF	An Introduction To The Theory Of Numbers	2008	G. H. Hardy E. M. Wright	10
+ PDF	Integers without large prime factors	1993	Adolf Hildebrand Gérald Tenenbaum	9
+	The Difference between Consecutive Prime Numbers	1938	R. A. Rankin	8
+	Bemerkung zu der Arbeit �ber vollkommene Zahlen in Math. Ann. Bd. 133, S. 431?438 (1957)	1959	Eduard Wirsing	8
+	Probabilistic Number Theory I	1979	P. D. T. A. Elliott	8
+ PDF	Approximate Formulas for Some Functions of Prime Numbers	1963	D. S. J. Barkley Rosser Lowell Schoenfeld	8
+	On Distinguishing Prime Numbers from Composite Numbers	1983	Leonard M. Adleman Carl Pomerance Robert Rumely	8
+ PDF	On the normal number of prime factors of $\phi(n)$	1985	Paul Erdös Carl Pomerance	7
+	The Difference between Consecutive Prime Numbers, III	1947	R. A. Rankin	7
+	Almost all primes can be quickly certified	1986	S. Goldwasser Joe Kilian	7
+ PDF	A new lower bound for the pseudoprime counting function	1982	Carl Pomerance	7
+	On the greatest common divisor of a number and its sum of divisors	2011	Paul Pollack	7
+	On the proportion of numbers coprime to a given integer	2008	Paul Erdös Florian Luca Carl Pomerance	7
+	Analytic Number Theory	2004	Henryk Iwaniec Emmanuel Kowalski	7
+ PDF	On the periods of the linear congruential and power generators	2005	Pär Kurlberg Carl Pomerance	6
+	On the number of positive integers ≤ x and free of prime factors > y, II	1966	N.G. de Bruijn	6
+ PDF	On Euler’s totient function	1932	D. H. Lehmer	6
+ PDF	Multiplicative structure of values of the Euler function	2004	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski	6
+ PDF	PRODUCTS OF SHIFTED PRIMES SIMULTANEOUSLY TAKING PERFECT POWER VALUES	2012	Tristan Freiberg	6
+ PDF	On the Distribution of Pseudoprimes	1981	Carl Pomerance	6
+	On the Number of False Witnesses for a Composite Number	1986	Paul Erdös Carl Pomerance	6
+ PDF	Strong Carmichael numbers	1976	D. H. Lehmer	6
+ PDF	The exceptional set of Goldbach's problem	1975	H. Montgomery R. C. Vaughan	6
+	p+a without large prime factors.	1984	Antal Balog	6
+ PDF	The fractional parts of the bernoulli numbers	1980	P. Erdős Samuel S. Wagstaff	6