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A073024 Primes p such that p-1 has a prime factor q > p^(2/3). 3
11, 23, 47, 59, 83, 107, 149, 167, 173, 179, 223, 227, 263, 269, 283, 293, 317, 347, 359, 367, 383, 389, 439, 467, 479, 499, 503, 509, 557, 563, 569, 587, 607, 619, 643, 653, 719, 773, 787, 797, 809, 823, 839, 857, 863, 887, 907, 983, 1019, 1031, 1039, 1049, 1087, 1091 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Etienne Fouvry showed that a positive fraction of all primes have this property.

REFERENCES

Etienne Fouvry, Theoreme de Brun-Titchmarsh: application au theoreme de Fermat, Invent. Math. 79 (1985), no. 2, 383-407.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..27449.

MAPLE

with(numtheory); a := []; for i from 2 to 1000 do p := ithprime(i); t1 := factorset(p-1); q := t1[nops(t1)]; if q^3 > p^2 then a := [op(a), p]; fi; od:

PROG

(PARI) gpf(n)=my(f=factor(n)[, 1]); f[#f]

is(n)=gpf(n-1)^3>n^2 && isprime(n) \\ Charles R Greathouse IV, Sep 14 2015

CROSSREFS

Cf. A005384, A005385, A073025, A073026.

Sequence in context: A334829 A068231 A185005 * A161897 A282531 A309851

Adjacent sequences:  A073021 A073022 A073023 * A073025 A073026 A073027

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 23 2002

STATUS

approved

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Last modified July 28 23:26 EDT 2021. Contains 346340 sequences. (Running on oeis4.)