A380333 Where prime race 8m+3 vs. 8m+7 is tied.

2, 7, 31, 37, 41, 47, 53, 79, 103, 127, 199, 223, 239, 241, 263, 269, 283, 293, 311, 313, 317, 367, 373, 383, 389, 397, 401, 409, 431, 433, 443, 449, 457, 461, 467, 499, 523, 541, 1039, 1049, 1063, 1069, 1091, 1093, 1097, 1123, 1129, 1163, 1231, 1237, 1249

Offset: 1

Author

Ya-Ping Lu, Jan 21 2025

Keywords

• nonn

Comments

Prime numbers on the y-axis of the Cartesian grid defined in A379643.

Conjecture: There is no prime on the negative y-axis of the Cartesian grid defined in A379643, meaning that prime p does not exist such that pi_{8,3}(p) - pi_{8,7}(p) = 0 and pi_{8,5}(p) - pi_{8,1}(p) < 0, where pi_{m,b}(x) is the number of primes <= x which are congruent to b (mod m).

Crossrefs

Cf. A379643, A379731, A379989.

Programs

Python

from sympy import nextprime; p, x = 2, 0; R = [p]
while p < 1249:
    p = nextprime(p); d = (5-p%8)//2
    if d in {-1, 1}: x += d
    if x == 0: R.append(p)
print(*R, sep = ', ')