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Least number such that a(n) and nextprime(a(n)) differ by at least a power of 10, 10^m, where m >= n.
2

%I #23 Oct 28 2021 13:25:41

%S 2,113,370261,1693182318746371

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

%C 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

%H Thomas R. Nicely, <a href="/A007053/a007053_1.pdf">Some Results of Computational Research in Prime Numbers</a> [Local copy, pdf only] [ See local copy in A007053]

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

%o (PARI) a(n) = {my(p = 2); while (nextprime(p+1) - p < 10^n, p = nextprime(p+1)); p;} \\ _Michel Marcus_, Jan 29 2016

%Y Cf. A002386, A034386.

%K nonn,hard,more

%O 0,1

%A _Jeff Burch_, Apr 02 2000

%E Definition clarified by _Michel Marcus_, Jan 29 2016

%E Definition clarified by _Chai Wah Wu_, Jun 26 2019