A396248

Created: 5/27/2026 | Author: Vincenzo Manto , May 20 2026

Primes prime(k) such that prime(k) - prime(k-1) is a factorial.

The sequence consists of all primes prime(k) for which the gap to the previous prime prime(k-1) is a factorial.Every upper member of a twin prime (A006512) pair belongs to the sequence, since 2 = 2!.

Sequence Chart

Data

3,5,7,13,19,29,31,37,43,53,59,61,67,73,79,89,103,109,137,139,151,157,163,173,179,181,193,199,229,239,241,257,263,269,271,277,283,313,337,349,359,373,379,389,421,433,439,449,463,509,523,547,563,569,571,577

Computational Implementations

PYTHON

from sympy import prime
import math
def sequence(n_max):
    results = []
    facts = [math.factorial(k) for k in range(0, 7)]
    for i in range(2, n_max + 1):
        gap = prime(i) - prime(i-1)
        if gap in facts:
            results.append(prime(i))
    return results
print(sequence(200))

Mathematica