A338578 Primes p such that (r-p)*(r-q) > r, where q and r are the next two primes.

2, 3, 5, 11, 17, 19, 29, 43, 47, 83, 109, 199, 283

Offset: 1

Author

Robert Israel, Nov 03 2020

Keywords

• nonn
• more

Comments

a(14) > 10^8 if it exists.

As soon as the prime gap grows slow enough, for all large enough p we have (r-p)*(r-q) <= r, implying finiteness of this sequence. In particular, finiteness would follow from Cramer's conjecture. - Max Alekseyev, Nov 09 2024

Examples

			a(5)=17 is a member because it is prime, the next two primes are 19 and 23, and (23-17)*(23-19)=24 > 23.
		

Crossrefs

Contains A338566.

Cf. A013632, A105161, A338577.

Programs

Maple

p:= 0: q:=2:r:= 3:  R:= NULL:
while p < 10^4 do
  p:= q: q:= r: r:= nextprime(r);
  if (r-q)*(r-p) > r then R:= R, p; fi
od:
R;