Mersenne+primtal

Mersenne primtal och perfekta tal.

@http://dictionary.reference.com/browse/quattuordecillion @http://arstechnica.com/science/2013/02/volunteer-discovers-a-new-17-million-digit-prime-number/

@http://www.mersenne.org/ Here is a list of the Mersenne primes 1-48 ( 48th was published Jan 2013 ). @http://mathworld.wolfram.com/MersennePrime.html

digits year discoverer value
 * # || p || digits || ..year || (reference) || value || perfect nbr ||  ||
 * 1 || 2 || 1 ||  || antiquity || 3 || 6 ||   ||
 * 2 || 3 || 1 ||  || antiquity || 7 || 28 ||   ||
 * 3 || 5 || 2 ||  || antiquity || 31 ||   ||   ||
 * 4 || 7 || 3 ||  || antiquity || 127 ||   ||   ||
 * 5 || 13 || 4 || 1461 || Reguis (1536), Cataldi (1603) || 8191 ||  ||   ||
 * 5 || 17 || 6 || 1588 || Cataldi (1603) || 131071 ||  ||   ||
 * 6 || 19 || 6 || 1588 || Cataldi (1603) || 524287 ||  ||   ||
 * 7 || 31 || 10 || 1750 || Euler (1772) || 2147483647 ||  ||   ||
 * 8 || 61 || 19 || 1883 || Pervouchine (1883), Seelhoff (1886) || 2305843009213693951 ||  ||   ||
 * 9 || 89 || 89 || 1911 || Powers (1911) || 618970019642690137449562111 ||  ||   ||
 * ||  ||   ||   ||   || 162259276829213363391578010288127 ||   ||   ||
 * ||  ||   ||   ||   || 170141183460469231731687303715884105727 ||   ||   ||
 * ||  ||   ||   ||   || 68647976601306097149...12574028291115057151 ||   ||   ||
 * ||  ||   ||   ||   || 68647976601306097149...12574028291115057151 ||   ||   ||

10 89 27 1911 Powers (1911) 618970019642690137449562111 11 107 33 1913 Powers (1914) 162259276829213363391578010288127 12 127 39 1876 Lucas (1876) 170141183460469231731687303715884105727 13 521 157 Jan. 30, 1952 Robinson (1954) 68647976601306097149...12574028291115057151 14 607 183 Jan. 30, 1952 Robinson (1954) 53113799281676709868...70835393219031728127 15 1279 386 Jun. 25, 1952 Robinson (1954) 10407932194664399081...20710555703168729087 16 2203 664 Oct. 7, 1952 Robinson (1954) 14759799152141802350...50419497686697771007 17 2281 687 Oct. 9, 1952 Robinson (1954) 44608755718375842957...64133172418132836351 18 3217 969 Sep. 8, 1957 Riesel 25911708601320262777...46160677362909315071 19 4253 1281 Nov. 3, 1961 Hurwitz 19079700752443907380...76034687815350484991 20 4423 1332 Nov. 3, 1961 Hurwitz 28554254222827961390...10231057902608580607

21 9689 2917 May 11, 1963 Gillies (1964) 47822027880546120295...18992696826225754111 22 9941 2993 May 16, 1963 Gillies (1964) 34608828249085121524...19426224883789463551 23 11213 3376 Jun. 2, 1963 Gillies (1964) 28141120136973731333...67391476087696392191 24 19937 6002 Mar. 4, 1971 Tuckerman (1971) 43154247973881626480...36741539030968041471 25 21701 6533 Oct. 30, 1978 Noll and Nickel (1980) 44867916611904333479...57410828353511882751 26 23209 6987 Feb. 9, 1979 Noll (Noll and Nickel 1980) 40287411577898877818...36743355523779264511 27 44497 13395 Apr. 8, 1979 Nelson and Slowinski 85450982430363380319...44867686961011228671 28 86243 25962 Sep. 25, 1982 Slowinski 53692799550275632152...99857021709433438207 29 110503 33265 Jan. 28, 1988 Colquitt and Welsh (1991) 52192831334175505976...69951621083465515007 30 132049 39751 Sep. 20, 1983 Slowinski 51274027626932072381...52138578455730061311

31 216091 65050 Sep. 6, 1985 Slowinski 74609310306466134368...91336204103815528447 32 756839 227832 Feb. 19, 1992 Slowinski and Gage 17413590682008709732...02603793328544677887 33 859433 258716 Jan. 10, 1994 Slowinski and Gage 12949812560420764966...02414267243500142591 34 1257787 378632 Sep. 3, 1996 Slowinski and Gage 41224577362142867472...31257188976089366527 35 1398269 420921 Nov. 12, 1996 Joel Armengaud/GIMPS 81471756441257307514...85532025868451315711 36 2976221 895832 Aug. 24, 1997 Gordon Spence/GIMPS 62334007624857864988...76506256743729201151 37 3021377 909526 Jan. 27, 1998 Roland Clarkson/GIMPS 12741168303009336743...25422631973024694271 38 6972593 2098960 Jun. 1, 1999 Nayan Hajratwala/GIMPS 43707574412708137883...35366526142924193791 39 13466917 4053946 Nov. 14, 2001 Michael Cameron/GIMPS 92494773800670132224...30073855470256259071 40 20996011 6320430 Nov. 17, 2003 Michael Shafer/GIMPS 12597689545033010502...94714065762855682047

41* 24036583 7235733 May 15, 2004 Josh Findley/GIMPS 29941042940415717208...67436921882733969407 42* 25964951 7816230 Feb. 18, 2005 Martin Nowak/GIMPS 12216463006127794810...98933257280577077247 43? 30402457 9152052 Dec. 15, 2005 Curtis Cooper and Steven Boone/GIMPS 31541647561884608093...11134297411652943871 44? 32582657 9808358 Sep. 4, 2006 Curtis Cooper and Steven Boone/GIMPS 12457502601536945540...11752880154053967871 45? 37156667 11185272 Sep. 6, 2008 Hans-Michael Elvenich/GIMPS 20225440689097733553...21340265022308220927 46? 42643801 12837064 Jun. 12, 2009 Odd Magnar Strindmo/GIMPS 16987351645274162247...84101954765562314751 47? 43112609 12978189 Aug. 23, 2008 Edson Smith/GIMPS 31647026933025592314...80022181166697152511 48? 57885161 17425170 Jan 25, 2013

*) Proven according to GIMPS not yet noted in Mathworld


 * The perfect numbers associated with these :**

Rank p Perfect number Digits Year Discoverer 1 2 6 1 Known to the Greeks[5] 2 3 28 2 Known to the Greeks 3 5 496 3 Known to the Greeks 4 7 8128 4 Known to the Greeks 5 13 33550336 8 1456 First seen in the medieval manuscript, Codex Lat. Monac.[6] 6 17 8589869056 10 1588 Cataldi[1] 7 19 137438691328 12 1588 Cataldi[1] 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 2 0 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.

@http://en.wikipedia.org/wiki/List_of_perfect_numbers

@http://dictionary.reference.com/browse/quattuordecillion @http://arstechnica.com/science/2013/02/volunteer-discovers-a-new-17-million-digit-prime-number/


 * Names of Mersenne primes and perfect numbers ?**

@http://www.mersenne.org/ Here is a list of the Mersenne primes 1-48 ( 48th was published Jan 2013 ). @http://mathworld.wolfram.com/MersennePrime.html

Name http://www.isthe.com/chongo/tech/math/prime/mersenne.html