A152295 -id:A152295

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A152292

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

+10
5

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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.

LINKS

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

MAPLE

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

od:

Res; # Robert Israel, Mar 07 2018

MATHEMATICA

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

PROG

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

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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Dec 02 2008

STATUS

approved

A152388

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

+10
1

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..26.

MATHEMATICA

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 *)

CROSSREFS

Cf. A152292, A152293, A152294, A152295