A107023 -id:A107023 - cp's OEIS frontend

A107021 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7 are all primes.

2, 6449, 12119, 19709, 30389, 74699, 107699, 133499, 143609, 167759, 175349, 206369, 210209, 229739, 244589, 254279, 334289, 422069, 528509, 541529, 607319, 641969, 658349, 751529, 810539, 810809, 812849, 926669, 934259, 956909, 968729

Offset: 1

Zak Seidov, May 09 2005

nonn

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A107024: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 all prime; A107023: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 all prime; A107022: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 all prime; A107020: p, 2p+1, 4p+3, 6p+5 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).

Cf. A005384, A007700, A107020, A107022, A107023, A107024.

[p: p in PrimesUpTo(1000000)| IsPrime(2*p+1) and IsPrime(4*p+3) and IsPrime(6*p+5) and IsPrime(8*p+7)]; // Vincenzo Librandi, Nov 13 2010

fQ[n_]:=And@@PrimeQ[{2n+1,4n+3,6n+5,8n+7}];Select[Prime@Range@77000,fQ] (* Harvey P. Dale, Dec 16 2010 *)

More terms from Vincenzo Librandi, Apr 01 2010

A107020 Primes p such that 2p+1, 4p+3, 6p+5 are all primes.

Original entry on oeis.org

2, 11, 41, 1901, 2459, 5081, 5849, 6131, 6449, 8969, 9221, 10691, 12119, 13229, 14009, 14321, 14669, 15161, 18461, 19709, 20411, 21179, 22271, 23099, 24551, 25601, 30389, 37991, 39419, 41381, 43691, 44699, 52289, 55631, 56081, 58979

Offset: 1

Zak Seidov, May 09 2005

nonn

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A107024: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 all prime; A107023: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 all prime; A107022: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 all prime; A107020: p, 2p+1, 4p+3, 6p+5, 8p+7 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).

Cf. A005384, A007700, A107021, A107022, A107023, A107024.

[p: p in PrimesUpTo(1000000)| IsPrime(2*p+1) and IsPrime(4*p+3) and IsPrime(6*p+5) ]; // Vincenzo Librandi, Nov 13 2010

Select[Range[60000],AllTrue[{#,2#+1,4#+3,6#+5},PrimeQ]&] (* James C. McMahon, Feb 09 2024 *)

More terms from Vincenzo Librandi, Apr 01 2010

A107022 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 are all primes.

Original entry on oeis.org

2, 6449, 210209, 244589, 528509, 810539, 968729, 985109, 1316699, 1551899, 1743419, 2832629, 4094999, 4328459, 5608409, 6036869, 7077419, 7939829, 8176979, 8673569, 8789279, 9080189, 9797279, 10122419, 10309889, 10487969

Offset: 1

Zak Seidov, May 09 2005

nonn

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A107024: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 all prime; A107023: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 all prime; A107021: p, 2p+1, 4p+3, 6p+5, 8p+7 all prime;A107020: p, 2p+1, 4p+3, 6p+5 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).

Cf. A005384, A007700, A107020, A107021, A107023, A107024.

[p: p in PrimesUpTo(100000000)| IsPrime(2*p+1) and IsPrime(4*p+3) and IsPrime(6*p+5) and IsPrime(8*p+7)and IsPrime(10*p+9)]; // Vincenzo Librandi, Nov 13 2010

Select[Prime[Range[700000]],And@@PrimeQ[{2#+1,4#+3,6#+5,8#+7,10#+9}]&] (* Harvey P. Dale, Jun 19 2013 *)
Select[Prime[Range[700000]],AllTrue[Table[2n #+2n-1,{n,5}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 22 2018 *)

More terms from Vincenzo Librandi, Apr 01 2010

A107024 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 are all primes.

Original entry on oeis.org

4094999, 9080189, 63196349, 66383519, 177109379, 196068179, 310143959, 389825729, 528083219, 909696059, 937924259, 1080610439, 1318820159, 1342772969, 1824166469, 1921977329

Offset: 1

Zak Seidov, May 09 2005

nonn

Donovan Johnson, Table of n, a(n) for n = 1..200

Cf. A107023: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 all prime; A107022: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 all prime; A107021: p, 2p+1, 4p+3, 6p+5, 8p+7 all prime; A107020: p, 2p+1, 4p+3, 6p+5 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).

Cf. A005384, A007700, A107020-A107023.

cp's OEIS Frontend

A107021 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7 are all primes.

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Magma

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A107020 Primes p such that 2p+1, 4p+3, 6p+5 are all primes.

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Programs

Magma

Mathematica

Extensions

A107022 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 are all primes.

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Author

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Crossrefs

Programs

Magma

Mathematica

Extensions

A107024 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 are all primes.

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