A100420
Numbers n such that 30*n+{1,7,11,17,19,23,29} are all prime.
Original entry on oeis.org
22621, 103205, 149125, 237794, 288467, 321451, 364921, 373370, 404002, 851099, 985933, 1106235, 1594044, 1696874, 1780265, 1824421, 1851756, 2249881, 3112939, 3257538, 3397608, 3601651, 3747356, 4347340, 4710990, 4886284
Offset: 1
Ferenc Adorjan (fadorjan(AT)freemail.hu), Nov 19 2004
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[ n: n in [4..70000000 by 7] | forall{ q: q in [1, 7, 11, 17, 19, 23, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 24 2011
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Select[Range[5000000],And@@PrimeQ[30 #+{1,7,11,17,19,23,29}]&] (* Harvey P. Dale, Mar 06 2011 *)
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 1-2 of 2 results.
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