A157357 Products of 3 distinct triple-safe primes.

777239, 1555559, 3112199, 4409399, 10635959, 12192599, 23348519, 23796743, 30612839, 47610023, 48628127, 55778519, 67454423, 91581239, 95286263, 97290047, 99883319, 102996599, 104812679, 135002663, 137841647, 148398599, 162707543, 170450999, 172007639, 186520823

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

• nonn
• easy

Examples

			777239=23*47*719; 23, 47, and 719 are triple-safe prime numbers.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A157358, A001358, A005384, A005385, A006881, A007304, A066179, A111206, A157342, A157344, A157345, A157346, A157347, A157352, A157353, A157354, A157355, A157356

Programs

Mathematica

lst={};Do[If[Plus@@Last/@FactorInteger[n]==3,a=Length[First/@FactorInteger[n]];If[a==3,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];e=b[[3]];If[PrimeQ[cx=(c-1)/2]&&PrimeQ[cy=(cx-1)/2]&&PrimeQ[(cy-1)/2]&&PrimeQ[dx=(d-1)/2]&&PrimeQ[dy=(dx-1)/2]&&PrimeQ[(dy-1)/2]&&PrimeQ[ex=(e-1)/2]&&PrimeQ[ey=(ex-1)/2]&&PrimeQ[(ey-1)/2],AppendTo[lst,n]]]],{n,9!,11!}];lst

PARI

list(lim)=my(v=List(), P=select(p->isprime(p\2) && isprime(p\4) && isprime(p\8), primes([11, sqrtint(lim\11+1)-1])), p, q, t); for(i=1, #P, p=P[i]; if(p^3>=lim, break); for(j=i+1, #P, q=P[j]; t=p*q; forprime(r=q+4, lim\t, if(isprime(r\2) && isprime(r\4) && isprime(r\8), listput(v, r*t))))); Set(v); \\ Charles R Greathouse IV, Oct 14 2021

Extensions

a(5)-a(26) from Charles R Greathouse IV, Oct 14 2021