Another chain of twin primes.
3, 5, 11, 59, 179, 1619, 9719, 417959, 7523279, 308454479, 25293267359, 1593475843679, 74893364652959, 4793175337789439, 517662936481259519, 21224180395731640319, 4075042635980474941439, 611256395397071241215999, 55624331981133482950655999
1
We start with p = 3, and take the next value of p to be k*p, where k > 1 is the least number that makes k*p-1 and k*p+1 prime.
T. D. Noe, Plot of 100 terms
T. D. Noe, Table of 100 terms
Eric W. Weisstein, MathWorld: Twin Primes
(Mma) p = 3; Join[{p}, Table[k = 2; While[! (PrimeQ[k*p - 1] && PrimeQ[k*p + 1]), k++]; p = k*p; p-1, {19}]]
Cf. S000304.
nonn,nice
T. D. Noe, Oct 17 2014