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

1,1

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

Links

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

Example

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.

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]

Prog

(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

Crossrefs

Cf. A123921.

Sequence in context: A141890 A056248 A126575 * A335737 A277607 A139889

Adjacent sequences: A229610 A229611 A229612 * A229614 A229615 A229616

Keyword

nonn

Author

K. D. Bajpai, Sep 26 2013

Status

approved