A093743
Number of prime pairs below 10^n having a difference of 16.
Original entry on oeis.org
0, 0, 0, 33, 339, 2881, 25099, 215804, 1846097, 15888305, 137715130, 1202533145, 10576414202, 93649741408, 834451865580, 7478286927272, 67376249426987, 609996708149171
Offset: 1
a(4) = 33 because there are 33 prime gaps of 16 below 10^3.
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20 N=1:dim T(34); 30 A=nxtprm(N); 40 N=A; 50 B=nxtprm(N); 60 D=B-A; 70 for x=2 to 34 step 2; 80 if D=X and B<10^2+1 then T(X)=T(X)+1; 90 next X; 100 if B>10^2+1 then 140; 110 B=A; 120 N=N+1; 130 goto 30; 140 for x=2 to 34 step 2; 150 print T(X);, 160 next (This program simultaneously finds values from 2 to 34 - if gap=2 add 1- adjust lines 80 and 100 for desired 10^n)
a(14)-a(18) from S. Herzog's website added by
Giovanni Resta, Aug 14 2018
A093744
Number of prime pairs below 10^n having a difference of 18.
Original entry on oeis.org
0, 0, 1, 40, 514, 4909, 43851, 384738, 3351032, 29189691, 255371697, 2246576317, 19878698732, 176913444597, 1583135619012, 14240370591853, 128711774414592, 1168583066366245
Offset: 1
a(4) = 40 because there are 40 prime gaps of 18 below 10^4.
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Table[Count[Differences[Prime[Range[PrimePi[10^n]]]],18],{n,8}] (* The program generates the first 8 terms in the sequence. To generate more increase the n constant but the program may take a long time to run. *) (* Harvey P. Dale, Sep 03 2021 *)
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20 N=1:dim T(34); 30 A=nxtprm(N); 40 N=A; 50 B=nxtprm(N); 60 D=B-A; 70 for x=2 to 34 step 2; 80 if D=X and B<10^2+1 then T(X)=T(X)+1; 90 next X; 100 if B>10^2+1 then 140; 110 B=A; 120 N=N+1; 130 goto 30; 140 for x=2 to 34 step 2; 150 print T(X);, 160 next (This program simultaneously finds values from 2 to 34 - if gap=2 add 1- adjust lines 80 and 100 for desired 10^n)
a(14)-a(18) from S. Herzog's website added by
Giovanni Resta, Aug 14 2018
A093745
Number of prime pairs below 10^n having a difference of 20.
Original entry on oeis.org
0, 0, 1, 15, 238, 2401, 22084, 202922, 1824043, 16296072, 145357801, 1298682892, 11638466683, 104682551230, 945244226939, 8568535834789, 77968773245740, 712064159940996
Offset: 1
a(4) = 15 because there are 15 prime gaps of 20 below 10^4.
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Table[Length[Select[Partition[Prime[Range[PrimePi[10^i]]], 2, 1], #[[2]] - #[[1]] == 20 &]], {i, 9}] (* Harvey P. Dale, Jan 29 2011 *)
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20 N=1:dim T(34); 30 A=nxtprm(N); 40 N=A; 50 B=nxtprm(N); 60 D=B-A; 70 for x=2 to 34 step 2; 80 if D=X and B<10^2+1 then T(X)=T(X)+1; 90 next X; 100 if B>10^2+1 then 140; 110 B=A; 120 N=N+1; 130 goto 30; 140 for x=2 to 34 step 2; 150 print T(X);, 160 next (This program simultaneously finds values from 2 to 34 - if gap=2 add 1- adjust lines 80 and 100 for desired 10^n)
a(14)-a(18) from S. Herzog's website added by
Giovanni Resta, Aug 14 2018
A093746
Number of prime pairs below 10^n having a difference of 22.
Original entry on oeis.org
0, 0, 0, 16, 223, 2172, 19451, 175945, 1569679, 13954281, 124059643, 1105634145, 9888091790, 88792328084, 800651549083, 7249252855793, 65896837322878, 601279985076759
Offset: 1
a(4) = 16 because there are 16 prime gaps of 22 below 10^4.
a(14)-a(18) from S. Herzog's website added by
Giovanni Resta, Aug 14 2018
A093747
Number of prime pairs below 10^n having a difference of 24.
Original entry on oeis.org
0, 0, 0, 15, 206, 2682, 27170, 257548, 2367474, 21487314, 194202685, 1754011594, 15861755259, 143759801949, 1306540582093, 11910121180550, 108905308434147, 998874124565038
Offset: 1
a(4) = 15 because there are 15 prime gaps of 24 below 10^4.
a(14)-a(18) from S. Herzog's website added by
Giovanni Resta, Aug 14 2018
A093748
Number of prime pairs below 10^n having a difference of 26.
Original entry on oeis.org
0, 0, 0, 3, 88, 1175, 12249, 119465, 1119585, 10347754, 94842255, 866077378, 7902711871, 72161896629, 659999185093, 6049187645033, 55574520617432, 511833282299754
Offset: 1
a(4) = 3 because there are 3 prime gaps of 26 below 10^n.
a(14)-a(18) from S. Herzog's website added by
Giovanni Resta, Aug 14 2018
A093749
Number of prime pairs below 10^n having a difference of 28.
Original entry on oeis.org
0, 0, 0, 5, 98, 1234, 13255, 129567, 1219243, 11287965, 103578486, 946685407, 8643973155, 78973715102, 722623290887, 6625617932534, 60889631777778, 560938901663498
Offset: 1
a(5) = 98 because there are 98 prime gaps of 28 below 10^5.
a(14)-a(18) from S. Herzog's website added by
Giovanni Resta, Aug 14 2018
A093750
Number of prime pairs below 10^n having a difference of 30.
Original entry on oeis.org
0, 0, 0, 11, 146, 1914, 21741, 222847, 2177991, 20706430, 194021497, 1803413614, 16694681959, 154292579858, 1425648765821, 13181528127233, 122022749987917, 1131306675851868
Offset: 1
a(5) = 146 because there are 146 prime gaps of 30 below 10^5.
a(14)-a(18) from S. Herzog's website added by
Giovanni Resta, Aug 14 2018
A093751
Number of prime pairs below 10^n having a difference of 32.
Original entry on oeis.org
0, 0, 0, 1, 32, 550, 6364, 68291, 683896, 6641319, 63276295, 596278790, 5582122930, 52074517134, 484995150904, 4514960515811, 42043818101407, 391829984349446
Offset: 1
a(5) = 32 because there are 32 prime gaps of 32 below 10^n.
a(14)-a(18) from S. Herzog's website added by
Giovanni Resta, Aug 14 2018
A093752
Number of prime pairs below 10^n having a difference of 34.
Original entry on oeis.org
0, 0, 0, 2, 33, 557, 6721, 71248, 719531, 6996756, 66745265, 629634308, 5900013825, 55082083947, 513336390285, 4781421106831, 44546412612392, 415327075240821
Offset: 1
a(5) = 33 because there are 33 prime gaps of 34 below 10^n.
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Table[Count[Differences[Prime[Range[PrimePi[10^n]]]],34],{n,13}] (* The program takes a long time to run *) (* Harvey P. Dale, Nov 24 2017 *)
a(14)-a(18) from S. Herzog's website added by
Giovanni Resta, Aug 14 2018