A152294 -id:A152294 - cp's OEIS frontend

A152292 Primes p of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=2.

17, 23, 59, 89, 239, 269, 293, 383, 419, 503, 953, 1013, 1193, 1259, 1823, 1979, 2129, 2633, 2789, 3209, 3389, 4229, 5099, 5333, 6089, 6299, 6803, 7019, 7673, 7853, 8123, 8513, 8753, 8819, 9059, 9203, 10169, 10223, 10589, 10853, 10979, 11159, 12689

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 02 2008

nonn

This is the general form : (p-n)/(n+1)=prime and (n+1)*p+n=prime; 'Safe' primes and 'Sophie Germain' primes just one part of this general form; If n=1 then we got 'Safe' primes and 'Sophie Germain' primes.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A059455, A152293, A152294, A152295, A152388.

[NthPrime(n): n in [5..2*10^3] | IsPrime(NthPrime(n) div 3) and IsPrime(3*NthPrime(n)+2)]; // Vincenzo Librandi, Mar 08 2018

Res:= NULL: count:= 0:
q:= 1:
while count < 100 do
q:= nextprime(q);
if isprime(3*q+2) and isprime(9*q+8)
    then Res:= Res, 3*q+2; count:= count+1
  fi
od:
Res; # Robert Israel, Mar 07 2018

lst={};n=2;Do[p=Prime[k];If[PrimeQ[(p-n)/(n+1)]&&PrimeQ[(n+1)*p+n],AppendTo[lst,p]],{k,7!}];lst

lista(nn) = forprime(p=17, nn, if(isprime(3*p+2) && isprime(p\3), print1(p", "))); \\ Altug Alkan, Mar 07 2018

A152295 Primes of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=5.

Original entry on oeis.org

17, 71, 83, 107, 191, 227, 251, 263, 431, 443, 479, 503, 587, 827, 839, 911, 983, 1091, 1151, 1163, 1187, 1619, 1667, 1847, 1907, 2087, 2243, 2459, 2591, 3023, 3467, 4463, 4871, 4943, 5471, 5519, 5651, 5807, 5903, 6131, 6203, 6299, 6311, 6563, 6983, 7127

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 02 2008

nonn

This is the general form : (p-n)/(n+1)=primeand(n+1)*p+n=prime; 'Safe' primes and'Sophie Germain' primes just one part of this general form; If n=1 then we got'Safe' primes and'Sophie Germain' primes.

Harvey P. Dale, Table of n, a(n) for n = 1..3000

Cf. A059455, A152292, A152293, A152294

lst={};n=5;Do[p=Prime[k];If[PrimeQ[(p-n)/(n+1)]&&PrimeQ[(n+1)*p+n],AppendTo[lst,p]],{k,7!}];lst
Select[Prime[Range[1000]],AllTrue[{(#-5)/6,6#+5},PrimeQ]&] (* This program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 29 2014 *)

A152388 Primes p such that (p-n)/(n+1) and (n+1)*p+n are both prime, with n=127.

Original entry on oeis.org

6143, 11519, 23039, 205823, 253439, 345599, 417023, 463103, 752639, 1071359, 1474559, 1511423, 1753343, 1766399, 1903103, 2188799, 2271743, 2711039, 2741759, 2747903, 2813183, 2997503, 3032063, 3258623, 3371519, 3463679

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 02 2008

nonn

This is the general form : (p-n)/(n+1)=primeand(n+1)*p+n=prime; 'Safe' primes and'Sophie Germain' primes just one part of this general form; If n=1 then we got'Safe' primes and'Sophie Germain' primes.

Cf. A152292, A152293, A152294, A152295

lst={};n=127;Do[p=Prime[k];If[PrimeQ[(p-n)/(n+1)]&&PrimeQ[(n+1)*p+n],AppendTo[lst,p]],{k,2*9!}];lst
Select[Prime[Range[250000]],AllTrue[{(#-127)/128,128#+127},PrimeQ]&] (* Harvey P. Dale, Apr 30 2023 *)

Definition clarified by Harvey P. Dale, Apr 30 2023

cp's OEIS Frontend

A152292 Primes p of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=2.

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A152295 Primes of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=5.

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A152388 Primes p such that (p-n)/(n+1) and (n+1)*p+n are both prime, with n=127.

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