A380877 Primes p where the prime race 12m+1 versus 12m+7 is tied.

2, 3, 5, 13, 17, 433, 457, 461, 27489101529397, 27489101529413, 27489101529493, 27489101534803, 27489101534953, 27489101534963, 27489101534969, 27489101535127, 27489101535131, 27489101535167, 27489101535221, 27489101536879, 27489101536909, 27489101536997

Offset

1,1

Comments

Primes p such that pi_{12,1}(p) = pi_{12,7}(p), where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m). For the first 5 billion primes, pi_{12,7}(p) >= pi_{12,1}(p). If exists, a(9) > 122430513841.

There are three regions below 10^19 where residues 1 and 7 (mod 12) are tied many times: 27489101529397 to 27555497263759, 97520543924496577 to 98977289882800319, and 108246985167355561 to 108251357023703549. - Benjamin Chaffin, Jun 11 2026

Links

Benjamin Chaffin, Table of n, a(n) for n = 1..10000

Mathematica

s={}; Do[p=Prime[pp]; If[Length[Select[Prime[Range[pp]], Mod[#, 12]==1&]]==Length[Select[Prime[Range[pp]], Mod[#, 12]==7&]], AppendTo[s, p]], {pp, 100}]; s (* James C. McMahon, Mar 03 2025 *)

Prog

(Python)
from sympy import nextprime; p, d = 2, 0
while p < 500:
    if d == 0: print(p, end = ', ')
    p = nextprime(p); r = p%12
    if r == 7: d += 1
    elif r == 1: d -= 1

Crossrefs

Cf. A007351, A068228, A068229, A379989, A380333.

Sequence in context: A073919 A162573 A349785 * A087356 A281598 A042261

Adjacent sequences: A380874 A380875 A380876 * A380878 A380879 A380880

Keyword

nonn,changed

Author

Ya-Ping Lu, Feb 06 2025

Extensions

a(9)-a(22) and onward from Benjamin Chaffin, Jun 11 2026

Status

approved