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 A093538 Number of primes between 10^n and 10^n+100. 2
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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 REFERENCES Marcus du Sautoy, "The Music of the Primes," HarperCollins, NY, 2003, page 6. LINKS Robert Israel, Table of n, a(n) for n = 0..4000 EXAMPLE a(7)=2 because there are 2 primes, 10000019 and 10000079, in the 100 numbers above 10000000. MAPLE q:= select(t -> t mod 3 <> 2 and igcd(t, 10)=1, [\$1..99]): f:= proc(n) local T;  T:= 10^n; numboccur(true, map(t -> isprime(T+t), q)) end proc: f(0):= 26: map(f, [\$0..100]); # Robert Israel, Feb 28 2020 CROSSREFS Cf. A323744. Sequence in context: A072360 A205322 A291470 * A220087 A022982 A023468 Adjacent sequences:  A093535 A093536 A093537 * A093539 A093540 A093541 KEYWORD nonn AUTHOR Jason Earls, May 14 2004 STATUS approved

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Last modified November 30 20:03 EST 2020. Contains 338812 sequences. (Running on oeis4.)