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%I #9 Feb 28 2020 22:56:29
%S 26,25,21,16,11,6,6,2,6,7,5,7,4,3,4,2,4,7,4,5,1,0,3,0,2,1,1,0,0,0,2,3,
%T 1,1,0,1,1,2,0,4,0,0,1,3,2,1,0,1,0,2,0,0,0,0,1,1,2,0,0,1,4,1,0,0,2,1,
%U 1,2,1,2,1,0,1,2,0,0,0,1,1,1,0,3,0,2,0,0,0,0,0,2,0,1,0,0,1,0,0,0,1,0,0,2,0
%N Number of primes between 10^n and 10^n+100.
%C Conjecture: a(n) = 1 for infinitely many n, but a(n)>=2 for only finitely many; in fact it may be that a(n)<=1 for n > 775. - _Robert Israel_, Feb 28 2020
%D Marcus du Sautoy, "The Music of the Primes," HarperCollins, NY, 2003, page 6.
%H Robert Israel, <a href="/A093538/b093538.txt">Table of n, a(n) for n = 0..4000</a>
%e a(7)=2 because there are 2 primes, 10000019 and 10000079, in the 100 numbers above 10000000.
%p q:= select(t -> t mod 3 <> 2 and igcd(t,10)=1, [$1..99]):
%p f:= proc(n) local T; T:= 10^n;
%p numboccur(true, map(t -> isprime(T+t),q))
%p end proc:
%p f(0):= 26:
%p map(f, [$0..100]); # _Robert Israel_, Feb 28 2020
%Y Cf. A323744.
%K nonn
%O 0,1
%A _Jason Earls_, May 14 2004
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