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 A002583 M0294 N0312 #58 Sep 08 2022 08:44:31
%S A002583 2,2,3,7,5,11,103,71,661,269,329891,39916801,2834329,75024347,
%T A002583 3790360487,46271341,1059511,1000357,123610951,1713311273363831,
%U A002583 117876683047,2703875815783,93799610095769647,148139754736864591,765041185860961084291,38681321803817920159601
%N A002583 Largest prime factor of n! + 1.
%C A002583 Theorem: For any N, there is a prime > N. Proof: Consider any prime factor of N!+1.
%C A002583 Cf. Wilson's theorem (1770): p | (p-1)! + 1 iff p is a prime.
%C A002583 If n is in A002981, then a(n) = n!+1. - _Chai Wah Wu_, Jul 15 2019
%D A002583 M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors).
%D A002583 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002583 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002583 Georg Fischer, <a href="/A002583/b002583.txt">Table of n, a(n) for n = 0..139</a> (first 101 terms originally derived from Hisanori Mishima's data by T. D. Noe)
%H A002583 A. Borning, <a href="http://dx.doi.org/10.1090/S0025-5718-1972-0308018-5 ">Some results for k!+-1 and 2.3.5...p+-1</a>, Math. Comp., 26 (1972), 567-570.
%H A002583 P. Erdős and C. L. Stewart, <a href="http://www.renyi.hu/~p_erdos/1976-27.pdf">On the greatest and least prime factors of n! + 1</a>, J. London Math. Soc. (2) 13:3 (1976), pp. 513-519.
%H A002583 M. Kraitchik, <a href="/A002582/a002582.pdf">On the divisibility of factorials</a>, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy]
%H A002583 Li Lai, <a href="https://arxiv.org/abs/2103.14894">On the largest prime divisor of n! + 1</a>, arXiv:2103.14894 [math.NT], 2021.
%H A002583 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha102.htm">Factorizations of many number sequences</a>
%H A002583 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha104.htm">Factorizations of many number sequences</a>
%H A002583 H. P. Robinson and N. J. A. Sloane, <a href="/A002037/a002037.pdf">Correspondence, 1971-1972</a>
%H A002583 Blake C. Stacey, <a href="https://doi.org/10.1007/978-3-030-76104-2_1">Equiangular Lines</a>, Ch. 1, A First Course in the Sporadic SICs, SpringerBriefs in Math. Phys. (2021) Vol. 41, see page 5.
%H A002583 R. G. Wilson v, <a href="/A038507/a038507.txt">Explicit factorizations</a>
%F A002583 Erdős & Stewart show that a(n) > n + (1-o(1))log n/log log n and lim sup a(n)/n > 2. - _Charles R Greathouse IV_, Dec 05 2012
%F A002583 Lai proves that lim sup a(n)/n > 7.238. - _Charles R Greathouse IV_, Jun 22 2021
%e A002583 (0!+1)=[2], (1!+1)=[2], (2!+1)=[3], (3!+1)=[7], (4!+1)=25=5*[5], (5!+1)=121=11*[11], (6!+1)=721=7*[103], (7!+1)=5041=71*[71], etc. - Mitch Cervinka (puritan(AT)toast.net), May 11 2009
%t A002583 PrimeFactors[n_]:=Flatten[Table[ #[[1]],{1}]&/@FactorInteger[n]]; Table[PrimeFactors[n!+1][[ -1]],{n,0,35}] ..and/or.. Table[FactorInteger[n!+1,FactorComplete->True][[ -1,1]],{n,0,35}] (* _Vladimir Joseph Stephan Orlovsky_, Aug 12 2009 *)
%t A002583 FactorInteger[#][[-1,1]]&/@(Range[0,30]!+1) (* _Harvey P. Dale_, Sep 04 2017 *)
%o A002583 (PARI) a(n)=my(f=factor(n!+1)[,1]);f[#f] \\ _Charles R Greathouse IV_, Dec 05 2012
%o A002583 (Magma) [Maximum(PrimeDivisors(Factorial(n)+1)): n in [0..30]]; // _Vincenzo Librandi_, Feb 14 2020
%Y A002583 Cf. A002582, A002981, A038507, A051301, A056111, A096225.
%K A002583 nonn,nice
%O A002583 0,1
%A A002583 _N. J. A. Sloane_
%E A002583 More terms from _Robert G. Wilson v_, Aug 01 2000
%E A002583 Corrected by _Jud McCranie_, Jan 03 2001