

A269261


Record (maximal) gaps between primes of the form 10k + 9.


2



10, 30, 80, 100, 110, 120, 170, 180, 190, 240, 270, 280, 290, 330, 360, 370, 500, 510, 610, 620, 630, 670, 700, 730, 840, 870, 950, 990, 1020, 1130, 1220, 1280, 1320, 1610, 1770, 1910, 2450
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OFFSET

1,1


COMMENTS

Dirichlet's theorem on arithmetic progressions suggests that average gaps between primes of the form 10k + 9 below x are about phi(10)*log(x). This sequence shows that the record gap ending at p grows almost as fast as phi(10)*log^2(p). Here phi(n) is A000010, Euler's totient function; phi(10)=4.
Conjecture: a(n) < phi(10)*log^2(A269263(n)) almost always.
A269262 lists the primes preceding the maximal gaps.
A269263 lists the corresponding primes at the end of the maximal gaps.


LINKS



EXAMPLE

The first two primes of the form 10k + 9 are 19 and 29, so a(1)=2919=10. The next prime of this form is 59 and the gap 5929=30 is a new record, so a(2)=30.


PROG

(PARI) re=0; s=19; forprime(p=29, 1e8, if(p%10!=9, next); g=ps; if(g>re, re=g; print1(g", ")); s=p)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



