A078500 Primes occurring only twice in a decade.

23, 29, 31, 37, 53, 59, 61, 67, 83, 89, 151, 157, 163, 167, 173, 179, 233, 239, 251, 257, 263, 269, 271, 277, 281, 283, 331, 337, 347, 349, 353, 359, 373, 379, 383, 389, 401, 409, 443, 449, 491, 499, 503, 509, 521, 523, 541, 547, 563, 569, 571, 577, 593, 599

Offset

1,1

Comments

Only 6 such primes will occur in the 21st century.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Mathematica

Select[Table[Prime[Range[PrimePi[n*10]+1, PrimePi[n*10+10]]], {n, 60}], Length[ #] == 2&]//Flatten (* Harvey P. Dale, Aug 09 2020 *)

Prog

(PARI) decade2pr(n1, n2) = { if(n1==0, n1=10); forstep(x=n1, n2, 10, if(isprime(x+1) && isprime(x+3) && !isprime(x+7) && !isprime(x+9), print1(x+1" "x+3" "); ); if(isprime(x+1) && isprime(x+7) && !isprime(x+3) && !isprime(x+9), print1(x+1" "x+7" "); ); if(isprime(x+1) && isprime(x+9) && !isprime(x+3) && !isprime(x+7), print1(x+1" "x+9" "); ); if(isprime(x+3) && isprime(x+7) && !isprime(x+1) && !isprime(x+9), print1(x+3" "x+7" "); ); if(isprime(x+3) && isprime(x+9) && !isprime(x+1) && !isprime(x+7), print1(x+3" "x+9" "); ); if(isprime(x+7) && isprime(x+9) && !isprime(x+1) && !isprime(x+3), print1(x+7" "x+9" "); ); ); }
(Magma) &cat [PrimesInInterval(10*n+1, 10*n+9): n in [0..50] | #PrimesInInterval(10*n+1, 10*n+9) eq 2]; // Bruno Berselli, Sep 05 2012

Crossrefs

Cf. A078494.

Sequence in context: A231073 A049483 A112681 * A155913 A227919 A240898

Adjacent sequences: A078497 A078498 A078499 * A078501 A078502 A078503

Keyword

nonn,easy,base

Author

Cino Hilliard, Jan 04 2003

Extensions

Offset changed to 1 by Alois P. Heinz, Jul 22 2014

Status

approved