A380333 -id:A380333 - cp's OEIS frontend

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

2, 3, 5, 13, 17, 433, 457, 461

Offset: 1

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Ya-Ping Lu, Feb 06 2025

nonn

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.

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

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 *)

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

cp's OEIS Frontend

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

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