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

5, 47, 113, 191, 293, 1117, 1487, 1733, 4057, 5153, 5737, 9767, 11633, 14321, 16607, 19013, 20681, 22469, 23677, 25561, 27191, 30937, 32369, 36833, 37991, 41959, 50591, 53327, 70717, 72869, 75037, 79493, 82889, 99191, 136861, 148957, 159167, 163979, 171341, 176369

Offset: 1

Author

K. D. Bajpai, Sep 26 2013

Keywords

• nonn

Comments

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.

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

Examples

			prime(4)*prime(5) - 30 = 7*11 - 30 = 47, which is prime, so 47 is a term.
prime(11)*prime(12) - 30 = 31*37 - 30 = 1117, which is prime, so 1117 is a term.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from K. D. Bajpai)

Crossrefs

Cf. A123921.

Programs

Maple

KD:= proc() local a; a:= ithprime(n)*ithprime(n+1)-30; if isprime((a)) then RETURN((a)):fi; end: seq(KD(),n=1..500);

Mathematica

Select[Table[Prime[n]*Prime[n + 1] - 30, {n, 100}], PrimeQ]

Python

from itertools import islice
from sympy import isprime, nextprime
def agen():
    p, q = 2, 3
    while True:
        t = p*q-30
        if isprime(t):
            yield t
        p, q = q, nextprime(q)
print(list(islice(agen(), 40))) # Michael S. Branicky, Jun 25 2022