A152292 -id:A152292 - cp's OEIS frontend

A152293 Primes of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=3.

11, 31, 47, 151, 271, 359, 439, 599, 719, 1031, 1759, 1871, 2287, 2711, 2767, 2879, 3719, 3911, 4079, 5119, 5527, 5791, 6199, 6271, 6991, 7151, 7607, 7727, 8447, 8647, 8831, 9151, 9391, 9511, 9839, 10159, 10687, 10847, 11279, 12479, 12919, 13487

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 02 2008

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. A059455, A152292

lst={};n=3;Do[p=Prime[k];If[PrimeQ[(p-n)/(n+1)]&&PrimeQ[(n+1)*p+n],AppendTo[lst,p]],{k,7!}];lst
Select[Prime[Range[1600]],AllTrue[{(#-3)/4,4#+3},PrimeQ]&] (* Harvey P. Dale, Aug 24 2025 *)

A152294 Primes of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=4.

Original entry on oeis.org

29, 89, 419, 509, 659, 1259, 1289, 1319, 1949, 2099, 2309, 2339, 2609, 2939, 3989, 4049, 6089, 6599, 7559, 8609, 9239, 9539, 10709, 12659, 12899, 13469, 13499, 18119, 20399, 21089, 21269, 21419, 22469, 23369, 26669, 27539, 28559, 30059, 30449

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. A059455, A152292, A152293.

lst={};n=4;Do[p=Prime[k];If[PrimeQ[(p-n)/(n+1)]&&PrimeQ[(n+1)*p+n],AppendTo[lst,p]],{k,7!}];lst

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

A152293 Primes of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=3.

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A152294 Primes of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=4.

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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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