Recent papers

Recent papers on the n²+1 prime conjecture, surfaced by the prominence of their authors in this directory.

Showing 15 papers, ranked by the Top 100 standing of their authors then by recency. Authors who appear in the Top 100 are shown in bold.

#	Title	Authors	Published	Best rank
1	Skolem Meets Bateman-Horn	Florian Luca, James Maynard, Armand Noubissie, Joël Ouaknine, James Worrell	2023-08	#2
2	Primitive root bias for twin primes II: Schinzel-type theorems for totient quotients and the sum-of-divisors function	Stephan Ramon Garcia, Florian Luca, Kye Shi, Gabe Udell	2019-06	#2
3	Primitive root biases for prime pairs I: existence and non-totality of biases	Stephan Ramon Garcia, Florian Luca, Timothy Schaaff	2017-08	#2
4	Primitive root bias for twin primes	Stephan Ramon Garcia, Elvis Kahoro, Florian Luca	2017-05	#2
5	Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1	Tim Browning, Efthymios Sofos, Joni Teräväinen	2022-12	#8
6	Schinzel Hypothesis on average and rational points	Alexei N. Skorobogatov, Efthymios Sofos	2020-05	#8
7	Cyclotomic polynomials with prescribed height and prime number theory	Alexandre Kosyak, Pieter Moree, Efthymios Sofos, Bin Zhang	2019-10	#8
8	Rational points and prime values of polynomials in moderately many variables	Kevin Destagnol, Efthymios Sofos	2018-01	#8
9	Serre's problem on the density of isotropic fibres in conic bundles	Efthymios Sofos	2016-02	#8
10	Level of distribution of unbalanced convolutions	Étienne Fouvry, Maksym Radziwiłł	2018-11	#9
11	On the exponent of distribution of the ternary divisor function	Étienne Fouvry, Emmanuel Kowalski, Philippe Michel	2013-04	#9
12	Fibonacci primes, primes of the form $2^n-k$ and beyond	Jon Grantham, Andrew Granville	2023-07	#13
13	An average Brun-Titchmarsh theorem and shifted primes with a large prime factor	Runbo Li	2025-08	#14
14	Largest square divisors of shifted primes	Runbo Li	2025-05	#14
15	On the largest prime factor of quadratic polynomials	Runbo Li	2024-06	#14

Most cited (all time)

The ten most-cited Mathematics works on the n²+1 prime conjecture, by citation count in OpenAlex. Results are filtered to the Mathematics field (OpenAlex field 26) and ranked by total citations.

The Top 100 ranking is designed to capture prominent, currently active researchers. If an author in this table is not linked to a profile, it is usually because they are deceased or less active than the researchers in the ranking, not because they are less significant to the field.

#	Title	Authors	Year	Citations
1	Almost-primes represented by quadratic polynomials DOI	Henryk Iwaniec	1978	136
2	Primes represented by quadratic polynomials in two variables DOI	Henryk Iwaniec	1974	54
3	Mean values of Dirichlet polynomials and applications to linear equations with prime variables DOI	Stephen Choi; Angel Kumchev	2006	37
4	A Report on Primes of the Form k⋅2 n + 1 and On Factors of Fermat Numbers DOI	Raphael M. Robinson	1958	32
5	Primes represented by irreducible polynomials in one variable DOI	Paul T. Bateman; Roger A. Horn	1965	31
6	New quadratic polynomials with high densities of prime values DOI	Michael J. Jacobson; Hugh C. Williams	2002	29
7	Primes are nonnegative values of a polynomial in 10 variables DOI	Yu. V. Matijasevič	1981	27
8	On prime valued polynomials and class numbers of real quadratic fields DOI	R. A. Mollin; Hywel C Williams	1988	27
9	Polynomial values free of large prime factors DOI	Cécile Dartyge; Gérald Tenenbaum; Greg Martin	2002	24
10	Quadratic polynomials which have a high density of prime values DOI	Gilbert Fung; Hywel C Williams	1990	24