A053976 Least number such that a(n) and nextprime(a(n)) differ by at least a power of 10, 10^m, where m >= n.

2, 113, 370261, 1693182318746371

Offset: 0

Author

Jeff Burch, Apr 02 2000

Keywords

• nonn
• hard
• more

Comments

a(4) <= 7910896513*A034386(283)/30 - 6480, a(5) <= 64279*A034386(3371)/5610 - 71678, a(6) <= 587*A034386(43103)/2310 - 455704 (using data from Nicely). - Chai Wah Wu, Jun 26 2019

Examples

			The primes following those shown are 3, 127, 370373, 1693182318747503. - _Michel Marcus_, Jan 29 2016
		

Links

• Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [Local copy, pdf only] [ See local copy in A007053]

Crossrefs

Cf. A002386, A034386.

Programs

PARI

a(n) = {my(p = 2); while (nextprime(p+1) - p < 10^n, p = nextprime(p+1)); p;} \\ Michel Marcus, Jan 29 2016

Extensions

Definition clarified by Michel Marcus, Jan 29 2016

Definition clarified by Chai Wah Wu, Jun 26 2019