OFFSET

2,1

COMMENTS

See A333586 for more information and references.

a(2) is the Skewes number for the so-called cousin primes.

The minimal span s(n) = pn - p1 of the n-tuples with an initial gap of 4 is s(2) = 4, s(3) = 6, s(4) = 10, s(5) = 12, s(6) = 16.

LINKS

PROG

(PARI) \\ Computes a(3)

Li(x, n)=intnum(t=2, n, 1/log(t)^x);

C3=0.635166354604271207206696591272522417342*(9/2); \\ A065418

p1=3; p2=5; n=0; forprime(p=7, 10^9, if(p-p1==6&&p-p2==2, n++; d=n-C3*Li(3, p2); if(d>=0, print(p1, " ", n, ">", C3*Li(3, p)); break)); p1=p2; p2=p)

CROSSREFS

KEYWORD

nonn,hard,more

AUTHOR

Hugo Pfoertner, Mar 30 2020

STATUS

approved