A107021
Primes p such that 2p+1, 4p+3, 6p+5, 8p+7 are all primes.
Original entry on oeis.org
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
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).
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[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
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fQ[n_]:=And@@PrimeQ[{2n+1,4n+3,6n+5,8n+7}];Select[Prime@Range@77000,fQ] (* Harvey P. Dale, Dec 16 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
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).
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[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
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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 *)
A107023
Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 are all primes.
Original entry on oeis.org
4094999, 9080189, 10957169, 11148899, 15917579, 19422059, 37267229, 37622339, 58680929, 63196349, 64595369, 66383519, 108463739, 177109379, 186977699, 189997079, 196068179, 228875849, 251891639, 261703889, 271031669, 310143959
Offset: 1
a(1) = p = 4094999 is a term because numbers i*p+(i-1), i=2(2)12 8189999,16379999,24569999,32759999,40949999,49139999 are all primes.
Cf.
A107024: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 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).
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s={};Do[p=Prime[i]; If[Union[PrimeQ[Table[i*p+(i-1),{i,2,12,2}]]]=={True},AppendTo[s,p]],{i,289435,1236230}];s
With[{t=Table[2n #+(2n-1),{n,6}]},Select[Prime[ Range[ 168*10^5]], AllTrue[ t,PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 14 2018 *)
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
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).
Showing 1-4 of 4 results.