A093538 - OEIS

A093538

Number of primes between 10^n and 10^n+100.

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

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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: