A153379 Larger of two consecutive prime numbers, p1 and p2 = p1 + d, such that p1*p2*d - d is the average of twin primes.

1193, 8923, 13997, 31847, 33113, 56039, 57593, 66593, 85843, 87803, 90583, 91229, 93503, 101323, 103183, 111697, 113123, 127453, 141403, 142897, 150373, 150413, 151673, 152623, 156823, 157133, 161983, 176849, 179743, 186013, 205963, 209431

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 24 2008

Keywords

• nonn

Examples

			1193 since 1187 and 1193 = 1187 + 6 are consecutive primes, 1187*1193*6 - 6 = 8496540, and (8496539, 8496541) are twin primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A099349, A153374, A153375, A153376, A153377, A153378.

Programs

Magma

[q:p in PrimesUpTo(210000)| IsPrime(a-1) and IsPrime(a+1) where a is (p*q-1)*(q-p) where q is NextPrime(p)]; // Marius A. Burtea, Jan 03 2020

Mathematica

lst={};Do[p1=Prime[n];p2=Prime[n+1];d=p2-p1;a=p1*p2*d-d;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p2]],{n,8!}];lst
l2cpQ[{a_,b_}]:=Module[{d=b-a},AllTrue[a*b*d-d+{1,-1},PrimeQ]]; Transpose[ Select[ Partition[Prime[Range[20000]],2,1],l2cpQ]][[2]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 18 2015 *)

Extensions

Name edited by Amiram Eldar, Jan 03 2020