cp's OEIS Frontend

A229613 Primes of the form p*q - 30, where p and q are consecutive primes.

%I A229613 #20 Jun 25 2022 17:08:44
%S A229613 5,47,113,191,293,1117,1487,1733,4057,5153,5737,9767,11633,14321,
%T A229613 16607,19013,20681,22469,23677,25561,27191,30937,32369,36833,37991,
%U A229613 41959,50591,53327,70717,72869,75037,79493,82889,99191,136861,148957,159167,163979,171341,176369
%N A229613 Primes of the form p*q - 30, where p and q are consecutive primes.
%C A229613 For primes p <= prime(5000) = 48611, the expression p*q - c with p and q consecutive primes yields more primes at c = 30 than at any other positive c <= 100.
%C A229613 For the above range of primes p, c=30 yields 999 primes, but there are values of c > 100 that yield larger counts; e.g., c = 210, 420, 2310, and 9240 yield 1129, 1194, 1295, and 1316, respectively. - _Jon E. Schoenfield_, Jun 25 2022
%H A229613 Michael S. Branicky, <a href="/A229613/b229613.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from K. D. Bajpai)
%e A229613 prime(4)*prime(5) - 30 = 7*11 - 30 = 47, which is prime, so 47 is a term.
%e A229613 prime(11)*prime(12) - 30 = 31*37 - 30 = 1117, which is prime, so 1117 is a term.
%p A229613 KD:= proc() local a; a:= ithprime(n)*ithprime(n+1)-30; if isprime((a)) then RETURN((a)):fi; end: seq(KD(),n=1..500);
%t A229613 Select[Table[Prime[n]*Prime[n + 1] - 30, {n, 100}], PrimeQ]
%o A229613 (Python)
%o A229613 from itertools import islice
%o A229613 from sympy import isprime, nextprime
%o A229613 def agen():
%o A229613     p, q = 2, 3
%o A229613     while True:
%o A229613         t = p*q-30
%o A229613         if isprime(t):
%o A229613             yield t
%o A229613         p, q = q, nextprime(q)
%o A229613 print(list(islice(agen(), 40))) # _Michael S. Branicky_, Jun 25 2022
%Y A229613 Cf. A123921.
%K A229613 nonn
%O A229613 1,1
%A A229613 _K. D. Bajpai_, Sep 26 2013