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

Author

Robert G. Wilson v, Oct 25 2003

Keywords

• nonn
• hard
• more

Comments

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

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

Examples

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

Links

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

Crossrefs

Cf. A087714, A088415, A093077.

Programs

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 *)

Extensions

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