A093078 - OEIS

%I #20 Dec 20 2022 11:59:29

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

%T 18869

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

%C a(19) > 22013. - _J.W.L. (Jan) Eerland_, Dec 19 2022

%C a(19) > 63317. - _J.W.L. (Jan) Eerland_, Dec 20 2022

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha107.htm">PI Pn - NextPrime (n = 1 to 100)</a>.

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

%t Do[p = Product[ Prime[i], {i, 1, n}]; q = Prime[n + 1]; If[ PrimeQ[p - q], Print[ Prime[n]]], {n, 1, 1435}]

%t 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 *)

%t 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 *)

%Y Cf. A087714, A088415, A093077.

%K nonn,hard,more

%O 1,1

%A _Robert G. Wilson v_, Oct 25 2003

%E a(16)-a(18) from _J.W.L. (Jan) Eerland_, Dec 19 2022