A093078 Primes p = prime(i) such that p(i)# - p(i+1) is prime.

5, 7, 11, 13, 19, 79, 83, 89, 149, 367, 431, 853, 4007, 8819, 8969, 12953, 18301, 18869

Offset

1,1

Comments

a(19) > 22013. - J.W.L. (Jan) Eerland, Dec 19 2022

a(19) > 63317. - J.W.L. (Jan) Eerland, Dec 20 2022

Links

Table of n, a(n) for n=1..18.

Hisanori Mishima, PI Pn - NextPrime (n = 1 to 100).

Example

3 = p(2) is in the sequence because p(2)# + p(3) = 11 is prime.

Mathematica

Do[p = Product[ Prime[i], {i, 1, n}]; q = Prime[n + 1]; If[ PrimeQ[p - q], Print[ Prime[n]]], {n, 1, 1435}]
Module[{nn=1120, pr1, pr2, prmrl}, pr1=Prime[Range[nn]]; pr2=Prime[Range[ 2, nn+1]]; prmrl=FoldList[Times, pr1]; Transpose[Select[Thread[{pr1, pr2, prmrl}], PrimeQ[#[[3]]-#[[2]]]&]][[1]]] (* Harvey P. Dale, Dec 07 2015 *)
n=1; Monitor[Parallelize[While[True, If[PrimeQ[Product[Prime[k], {k, 1, n}]-Prime[n + 1]], Print[Prime[n]]]; n++]; n], n] (* J.W.L. (Jan) Eerland, Dec 19 2022 *)

Crossrefs

Cf. A087714, A088415, A093077.

Sequence in context: A339347 A167460 A045439 * A314298 A314299 A349459

Adjacent sequences: A093075 A093076 A093077 * A093079 A093080 A093081

Keyword

nonn,hard,more

Author

Robert G. Wilson v, Oct 25 2003

Extensions

a(16)-a(18) from J.W.L. (Jan) Eerland, Dec 19 2022

Status

approved