A087714 Primes p = prime(i) such that p(i)# - p(i+1) and p(i)# + p(i+1) are both primes, where p# = A002110.

5, 13, 19, 367

Offset: 1

Author

Pierre CAMI, Sep 28 2003

Keywords

• nonn
• more

Comments

Conjecture: there are only 4 primes in this sequence.

Examples

			2*3*5-7 = 23 is prime, 2*3*5+7 = 37 is prime.
		

Crossrefs

Cf. A087715, A087716, A087728.

Cf. A002110.

Programs

PARI

isok(p) = {if (isprime(p), my(pp = prod(k=1, primepi(p), prime(k)), q = nextprime(p+1)); isprime(pp-q) && isprime(pp+q););} \\ Michel Marcus, Sep 20 2019

PARI

my(pr=1); forprime(p=1, , pr=pr*p; if(ispseudoprime(pr-nextprime(p+1)) && ispseudoprime(pr+nextprime(p+1)), print1(p, ", "))) \\ Felix Fröhlich, Sep 20 2019