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A380877
Primes p where the prime race 12m+1 versus 12m+7 is tied.
0
2, 3, 5, 13, 17, 433, 457, 461
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.
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
KEYWORD
nonn,new
AUTHOR
Ya-Ping Lu, Feb 06 2025
STATUS
approved