A140791
First occurrence of prime gap 10*n.
Original entry on oeis.org
139, 887, 4297, 19333, 31907, 43331, 173359, 542603, 404851, 396733, 1468277, 1895359, 5518687, 7621259, 13626257, 33803689, 27915737, 17051707, 142414669, 378043979, 20831323, 47326693, 607010093, 391995431, 387096133, 944192807
Offset: 1
- J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 139, pp 47, Ellipses, Paris 2008.
A058193
Smallest prime p such that there is a gap of 6n between p and the next prime.
Original entry on oeis.org
23, 199, 523, 1669, 4297, 9551, 16141, 28229, 35617, 43331, 162143, 31397, 188029, 461717, 404851, 360653, 1444309, 2238823, 492113, 1895359, 1671781, 1357201, 3826019, 11981443, 13626257, 17983717, 39175217, 37305713, 52721113
Offset: 1
d = 72 appears after 31397, while smaller d = 54, 60, 66 come later, following primes 35617, 43331, 162143, respectively.
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Module[{nn=32*10^5,prs,gps},prs=Prime[Range[nn]];gps=Differences[prs];Table[SelectFirst[Thread[{Most[prs],gps}],#[[2]]==6n&],{n,30}]][[;;,1]] (* Harvey P. Dale, Mar 03 2025 *)
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a(n) = {p=3; q = nextprime(p+1); while((q-p) != 6*n, p = q; q = nextprime(q+1)); p;} \\ Michel Marcus, Mar 12 2016
A101232
First occurrence of prime gap 10^n.
Original entry on oeis.org
2, 139, 396733, 22439962446379651
Offset: 0
A062530
Smallest prime p such that there is a gap of 2^n between p and previous prime.
Original entry on oeis.org
3, 5, 11, 97, 1847, 5623, 89753, 3851587, 1872852203, 1999066711903, 22790428875365903, 5333419265419188034369535864127397, 55128448018333565337014555712123010955456071077000028555991473847
Offset: 0
a(2) = 11 because 7 and 11 are consecutive primes with difference 4. - _Sascha Kurz_, Mar 05 2002
Further terms from Larry Reeves (larryr(AT)acm.org), Jun 13 2002
A204813
Primes followed by a gap of 256 = nextprime(p)-p.
Original entry on oeis.org
1872851947, 2362150363, 2394261637, 2880755131, 2891509333, 3353981623, 3512569873, 3727051753, 3847458487, 4008610423, 4486630573, 4541745583, 4755895531, 4837532347, 5227869607, 5389475977, 6201260587, 6229685347, 6952228483, 7325665111, 7414468513
Offset: 1
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list_gaps(g=256,f,N=25,p=0)=for(c=1,N,while(g+p!=p=nextprime(p+1),);if(f,write(f".txt",c" ",p-g),print1(", "p-g)))
A062531
Index of smallest prime p such that there is a gap of 2^n between p and next prime.
Original entry on oeis.org
2, 4, 24, 282, 738, 8688, 273413, 92276646, 73268943890, 622074604151528
Offset: 1
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