A100423
Numbers n such that 30*n+{1,7,11,13,17,19,29} are all prime.
Original entry on oeis.org
62, 188, 9491, 31982, 38226, 38520, 89459, 168237, 175125, 368248, 471078, 634892, 704416, 803102, 994748, 1436315, 1488857, 1605484, 1842553, 1945824, 2282958, 2465266, 2620715, 2627029, 2705037, 4282305, 5569899, 5914824
Offset: 1
Ferenc Adorjan (fadorjan(AT)freemail.hu), Nov 19 2004
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[ n: n in [0..6000000] | forall{ q: q in [1, 7, 11, 13, 17, 19, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 24 2011
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Select[Range[6*10^6],AllTrue[30#+{1,7,11,13,17,19,29},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 21 2021 *)
A100421
Numbers n such that 30*n+{1,7,11,13,19,23,29} are all prime.
Original entry on oeis.org
2, 79, 391701, 505017, 740413, 787187, 933025, 1169863, 1333719, 1406792, 2212261, 2719950, 2962738, 3125992, 3284955, 3384586, 3727271, 3821295, 3861881, 4320864, 4439878, 4764356, 5014865, 5480190, 5879274, 6124442
Offset: 1
Ferenc Adorjan (fadorjan(AT)freemail.hu), Nov 19 2004
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[ n: n in [2..70000000 by 7] | forall{ q: q in [1, 7, 11, 13, 19, 23, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 24 2011
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Select[Range[7*10^6],AllTrue[30#+{1,7,11,13,19,23,29},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 16 2016 *)
A385124
Numbers k such that there are exactly 7 primes between 30*k and 30*k+30.
Original entry on oeis.org
1, 2, 49, 62, 79, 89, 188, 6627, 9491, 18674, 22621, 31982, 34083, 38226, 38520, 41545, 48713, 53887, 89459, 103205, 114731, 123306, 139742, 140609, 149125, 168237, 175125, 210554, 223949, 229269, 237794, 240007, 267356, 288467, 321451, 364921, 368248, 373370, 391701
Offset: 1
1 is a term since there are 7 primes in 30..60: 31, 37, 41, 43, 47, 53, 59.
2 is a term since there are 7 primes in 60..90: 61, 67, 71, 73, 79, 83, 89.
3 is not a term since there are only 6 primes in 90..120: 97, 101, 103, 107, 109, 113.
49 is a term since there are 7 primes in 30*49..30*50: 1471, 1481, 1483, 1487, 1489, 1493, 1499.
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ArrayPlot[Table[Boole@PrimeQ[i*30+j],{i,0,399},{j,30}],Mesh->True]
index=1;Do[If[Length@(*PrimeRange=*) Select[Range[30*k+1,30*k+30,2],PrimeQ]==7,Print[index++," ",k]],{k,1,10^9}]
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[n|n<-[1..10^6],#primes([30*n,30*n+30])==7]
Showing 1-3 of 3 results.
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