Elèinc ed nùmer perfêt
Artéccol in dialètt mudnés
Chè 'd séguit, 'l elèinc di nùmer perfêt cgnusû infîn a incō, cun anca 'l esponèint p di prìm ed Mersenne ch'al i costruìs ind l'espresiòun 2p−1× (2p − 1), indû (2p − 1) 'l è al prìm ed Mersenne[1]. Tùt i nùmer perfêt i gh'àn cla forma chè. Infìn a 'l 2015, a s è rivê a cgnùser 48 nùmer perfêt in tùt.[2]
Órdin | p | Nùmer perfèt | Ciffri | An | Al só descuvridōr |
---|---|---|---|---|---|
1 | 2 | 6 | 1 | Cgnusû fin dai Grēc antîg[3] | |
2 | 3 | 28 | 2 | Cgnusû fin dai Grēc antîg | |
3 | 5 | 496 | 3 | Cgnusû fin dai Grēc antîg | |
4 | 7 | 8128 | 4 | Cgnusû fin dai Grēc antîg | |
5 | 13 | 33550336 | 8 | 1456 | Catê ind un manuscrìt medievêl, Codex Lat. Monac.[4] |
6 | 17 | 8589869056 | 10 | 1588 | Cataldi[5] |
7 | 19 | 137438691328 | 12 | 1588 | Cataldi |
8 | 31 | 2305843008139952128 | 19 | 1772 | Euler |
9 | 61 | 265845599…953842176 | 37 | 1883 | Pervushin |
10 | 89 | 191561942…548169216 | 54 | 1911 | Powers |
11 | 107 | 131640364…783728128 | 65 | 1914 | Powers |
12 | 127 | 144740111…199152128 | 77 | 1876 | Lucas |
13 | 521 | 235627234…555646976 | 314 | 1952 | Robinson |
14 | 607 | 141053783…537328128 | 366 | 1952 | Robinson |
15 | 1279 | 541625262…984291328 | 770 | 1952 | Robinson |
16 | 2203 | 108925835…453782528 | 1327 | 1952 | Robinson |
17 | 2281 | 994970543…139915776 | 1373 | 1952 | Robinson |
18 | 3217 | 335708321…628525056 | 1937 | 1957 | Riesel |
19 | 4253 | 182017490…133377536 | 2561 | 1961 | Hurwitz |
20 | 4423 | 407672717…912534528 | 2663 | 1961 | Hurwitz |
21 | 9689 | 114347317…429577216 | 5834 | 1963 | Gillies |
22 | 9941 | 598885496…073496576 | 5985 | 1963 | Gillies |
23 | 11213 | 395961321…691086336 | 6751 | 1963 | Gillies |
24 | 19937 | 931144559…271942656 | 12003 | 1971 | Tuckerman |
25 | 21701 | 100656497…141605376 | 13066 | 1978 | Noll & Nickel |
26 | 23209 | 811537765…941666816 | 13973 | 1979 | Noll |
27 | 44497 | 365093519…031827456 | 26790 | 1979 | Nelson & Slowinski |
28 | 86243 | 144145836…360406528 | 51924 | 1982 | Slowinski |
29 | 110503 | 136204582…603862528 | 66530 | 1988 | Colquitt & Welsh |
30 | 132049 | 131451295…774550016 | 79502 | 1983 | Slowinski |
31 | 216091 | 278327459…840880128 | 130100 | 1985 | Slowinski |
32 | 756839 | 151616570…565731328 | 455663 | 1992 | Slowinski & Gage |
33 | 859433 | 838488226…416167936 | 517430 | 1994 | Slowinski & Gage |
34 | 1257787 | 849732889…118704128 | 757263 | 1996 | Slowinski & Gage |
35 | 1398269 | 331882354…723375616 | 841842 | 1996 | Armengaud, Woltman, et al. |
36 | 2976221 | 194276425…174462976 | 1791864 | 1997 | Spence, Woltman, et al. |
37 | 3021377 | 811686848…022457856 | 1819050 | 1998 | Clarkson, Woltman, Kurowski, et al. |
38 | 6972593 | 955176030…123572736 | 4197919 | 1999 | Hajratwala, Woltman, Kurowski, et al. |
39 | 13466917 | 427764159…863021056 | 8107892 | 2001 | Cameron, Woltman, Kurowski, et al. |
40 | 20996011 | 793508909…206896128 | 12640858 | 2003 | Shafer, Woltman, Kurowski, et al. |
41 | 24036583 | 448233026…572950528 | 14471465 | 2004 | Findley, Woltman, Kurowski, et al. |
42 | 25964951 | 746209841…791088128 | 15632458 | 2005 | Nowak, Woltman, Kurowski, et al. |
43 | 30402457 | 497437765…164704256 | 18304103 | 2005 | Cooper, Boone, Woltman, Kurowski, et al. |
44 | 32582657 | 775946855…577120256 | 19616714 | 2006 | Cooper, Boone, Woltman, Kurowski, et al. |
45 | 37156667 | 204534225…074480128 | 22370543 | 2008 | Elvenich, Woltman, Kurowski, et al. |
46 | 42643801 | 144285057…377253376 | 25674127 | 2009 | Strindmo, Woltman, Kurowski, et al. |
47 | 43112609 | 500767156…145378816 | 25956377 | 2008 | Smith, Woltman, Kurowski, et al. |
48 | 57885161 | 169296395…270130176 | 34850340 | 2013 | Cooper, Woltman, Kurowski, et al. |
I nùmer perfêt elenchê chè in sìma i ìn quī ch'a s cgnùs infìn a 'l 2015. Se in dal futûr a in gnarà catê un quelchidùn èter, a 'l se prà śuntèr dôp o fórsi da mêś, ai ùltem quàter. Difât al GIMPS 'l à dìt che infîn a 'l 8 novèmber dal 2014 al catamèint 'd èter prìm ed Mersenne (e dòunca 'd èter nùmer perfêt) 'l è stê completê infîn ai prìm 44 edl elèinc.[6]
Vōś lighèdi
modificaReferèinsi
modifica- ↑ (EN) Primes: History, Theorems and Lists dal Chris Caldwell, in dal sît Prime Pages.
- ↑ (EN) 'L elèinc di nùmer perfêt publichê da 'l MIT.
- ↑ (EN) The Penguin's Dictionary of curious and interesting numbers alśìbil in sìm'a Google Books in dla réda.
- ↑ (EN) Divisibility and primality p. 6, dal Leonard Eugene Dickson (1999).
- ↑ (EN) 50 mathematical ideas you really need to know dal Tony Crilly, Quercus Publishing (2007), pàǵ 55.
- ↑ (EN) GIMPS Milestones Report.
Colegamèint estèren
modifica- (EN) Mersenne Primes: History, Theorems and Lists in dla réda.