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 A057588 Kummer numbers: -1 + product of first n consecutive primes. 30
 1, 5, 29, 209, 2309, 30029, 510509, 9699689, 223092869, 6469693229, 200560490129, 7420738134809, 304250263527209, 13082761331670029, 614889782588491409, 32589158477190044729, 1922760350154212639069 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is congruent to -1 modulo the first n primes. - Michael Engling, Mar 31 2011 Named after the German mathematician Ernst Eduard Kummer (1810-1893). - Amiram Eldar, Jun 19 2021 LINKS T. D. Noe, Table of n, a(n) for n = 1..100 E. E. Kummer, Neuer elementarer Beweis des Satzes, dass die Anzahl aller Primzahlen eine unendliche ist, Monatsber. Preuss. Akad. Wiss., Berlin 1878/9, pp. 777-778. [Collected Papers, II, pp. 669-670, Springer, Berlin-Heidelberg, 1975.] Cited in Mestrovic. Romeo Meštrović, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012. - From N. J. A. Sloane, Jun 13 2012 Hisanori Mishima, Factorizations of many number sequences. R. G. Wilson v, Explicit factorizations. FORMULA a(n) = A002110(n) - 1. - Altug Alkan, Oct 02 2015 MAPLE seq(mul(ithprime(k), k=1..n) - 1, n=1..100); # Muniru A Asiru, Jan 19 2018 MATHEMATICA Table[Product[Prime[k], {k, 1, n}] - 1, {n, 1, 18}] (* Artur Jasinski, Jan 01 2007 *) FoldList[Times, 1, Prime[Range[20]]]-1 (* Harvey P. Dale, Apr 17 2011 *) Table[ChineseRemainder[PadRight[{}, n, -1], Prime[Range[n]]], {n, 20}] (* Harvey P. Dale, Jul 01 2017 *) PROG (Haskell) a057588 = (subtract 1) . product . (flip take a000040_list) -- Reinhard Zumkeller, Mar 27 2013 (PARI) a(n) = prod(k=1, n, prime(k)) - 1; \\ Michel Marcus, Oct 02 2015 CROSSREFS Cf. A002110, A006862, A057705 (primes), A000040. Sequence in context: A301878 A331798 A103213 * A030522 A091124 A121143 Adjacent sequences: A057585 A057586 A057587 * A057589 A057590 A057591 KEYWORD nonn,easy,nice AUTHOR Mario Velucchi (mathchess(AT)velucchi.it), Oct 05 2000 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Oct 05 2000 STATUS approved

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Last modified November 30 00:02 EST 2022. Contains 358431 sequences. (Running on oeis4.)