

A087010


Number of primes of form 4*k+1 between n and 2n (inclusive).


3



0, 0, 1, 1, 1, 0, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 5, 6, 6, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 10, 9, 10, 10, 10, 9, 9
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OFFSET

1,9


COMMENTS

Erdős proved that between any n > 7 and its double there are always at least two primes, one of form 4*k+1 and one of form 4*k+3.


REFERENCES

B. Schechter, "My Brain is Open: The Mathematical Journeys of Paul Erdős," Simon & Schuster, New York, 1998, p. 62.


LINKS



MATHEMATICA

a[n_] := Module[{c = 0}, Do[If[Mod[k, 4] == 1 && PrimeQ[k], c++], {k, n, 2 n}]; c]; Array[a, 100] (* Amiram Eldar, Dec 16 2019 *)


PROG

(Magma) [#[p:p in PrimesInInterval(n, 2*n) p mod 4 eq 1]:n in [1..110]]; // Marius A. Burtea, Dec 16 2019


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



