This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A079296 #37 Feb 16 2025 08:32:48
%S A079296 7,113,23,13,31,3,1327,19,47,199,139,89,5,211,293,53,523,317,61,181,
%T A079296 73,887,1129,83,37,241,2,43,283,1669,11,467,1069,337,509,2477,131,
%U A079296 2179,2971,1259,773,1951,1637,409,3271,421,151,1381,67,839,619,863,157,17,661,3137
%N A079296 Primes ordered by decreasing value of the function p -> sqrt(q) - sqrt(p) where q is the next prime after p.
%C A079296 I computed a couple of thousand primes with EXCEL and ordered them accordingly. There is a very small chance that very large prime numbers will change the order of the given terms above.
%C A079296 This sequence only makes sense if the sequence n -> sqrt(p_(n+1)) - sqrt(p_n) is a zero-sequence which is a hard unsolved problem. See also Andrica's conjecture.
%C A079296 For each consecutive prime pair p < q, the number d = sqrt(q) - sqrt(p) is unique. Place d in order from greatest to least and specify p. See Table II in Wolf. A rearrangement of the primes. - _Robert G. Wilson v_, Oct 18 2012
%H A079296 Donovan Johnson, <a href="/A079296/b079296.txt">Table of n, a(n) for n = 1..10000</a>
%H A079296 C. K. Caldwell, <a href="http://www.utm.edu/research/primes/notes/gaps.html">Gaps between primes</a>.
%H A079296 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/AndricasConjecture.html">Andrica's Conjecture</a>
%H A079296 Wikipedia, <a href="http://en.wikipedia.org/wiki/Andrica's_conjecture">Andrica's conjecture</a>
%H A079296 Marek Wolf, <a href="http://arxiv.org/abs/1010.3945">A note on the Andrica conjecture</a>, arXiv:1010.3945 [math.NT], 2010.
%t A079296 lim = 1/5; lst = {}; p = 2; q = 3; While[p < 50000, If[ Sqrt[q] - Sqrt[p] > lim, AppendTo[lst, {p, Sqrt[q] - Sqrt[p]}]]; p = q; q = NextPrime[q]]; First@ Transpose@ Sort[lst, #1[[2]] > #2[[2]] &] (* _Robert G. Wilson v_, Oct 18 2012 *)
%Y A079296 Cf. A078692, A002386, A084974 (records).
%K A079296 nonn,nice
%O A079296 1,1
%A A079296 _Thomas Nordhaus_, Feb 09 2003
%E A079296 More terms from _Robert G. Wilson v_, Oct 18 2012