A137625 The initial prime in the first set of n consecutive primes for which p+4 is semiprime.

2, 29, 173, 709, 1741, 8297, 8297, 19213, 175229, 175229, 33952609, 4377722623, 4377722623, 1242030992173, 1242030992173

Offset

1,1

Comments

Suggested by Carlos Rivera's Puzzle 429 which asks for runs where p+2 is biprime.

Links

Table of n, a(n) for n=1..15.

Example

a(2)=29 because this is the first prime in a run of 2 where p+4 is semiprime (3*11).

Prog

(UBASIC) 10 'p+4 is biprime 20 N=1 30 A=3:S=sqrt(N) 40 B=N\A: if B*A=N then N=N+2:goto 30 50 A=A+2: if A<=S then 40 60 C=C+1:O=N+4:D=prmdiv(O):E=O\D 70 if E<>prmdiv(E) or E=1 then C=0:goto 90 80 print C; N; D; E; O: if C>=10 then stop 90 N=N+2:goto 30

Crossrefs

Cf. A001358, A137626, A137627, A137628.

Sequence in context: A308899 A028883 A024200 * A132412 A369384 A342454

Adjacent sequences: A137622 A137623 A137624 * A137626 A137627 A137628

Keyword

more,nonn

Author

Enoch Haga, Jan 30 2008

Extensions

a(1) corrected and a(11)-a(15) from Giovanni Resta, Jun 22 2018

Status

approved