Questa pagina contiene i risultati ottenuti negli anni durante la mia attività di ricerca nell'ambito della Teoria dei Numeri.
Tutte le informazioni inerenti agli avanzamenti, personali e del Team Italia (fondato dal sottoscritto e da Guido Lorenzini), relativi ai progetti distribuiti come GIMPS, FermatSearch e Operation Billion Digits trovano posto nelle relative pagine dei progetti.
Parte delle informazioni relative alla ricerca si trovano su The Prime Pages, il sito sui numeri primi gestito dal Prof. Chris Caldwell dell'Università del Tennesse at Martin.
1. Calcolo di primalità
2 * 205833 * (22976221 - 1 ) + 1
Possible prime factor of the double Mersenne number MM36 (222976221-1-1).
Unfortunately, this prime number of 895,938 digits does not divide MM36.
20th August 2017 (895,938 digits).
2 * 764648 * (2859433 - 1 ) + 1
Possible prime factor of the double Mersenne number MM33 (22859433-1-1).
Unfortunately, this prime number of 258,722 digits does not divide MM33.
26th July 2017 (258,722 digits).
2 * 1972572 * (2756839 - 1 ) + 1
Possible prime factor of the double Mersenne number MM32 (22756839-1-1).
Unfortunately, this prime number of 227,838 digits does not divide MM32.
28th June 2017 (227,838 digits).
2 * 1630328 * (2756839 - 1 ) + 1
Possible prime factor of the double Mersenne number MM32 (22756839-1-1).
Unfortunately, this prime number of 227,838 digits does not divide MM32.
18th May 2017 (227,838 digits).
2 * 1491308 * (21257787 - 1 ) + 1
Possible prime factor of the double Mersenne number MM34 (221257787-1-1).
Unfortunately, this prime number of 378,638 digits does not divide MM34.
20th June 2014 (378,638 digits).
2 * 544952 * (21257787 - 1 ) + 1
Possible prime factor of the double Mersenne number MM34 (221257787-1-1).
Unfortunately, this prime number of 378,638 digits does not divide MM34.
20th June 2014 (378,638 digits).
2 * 1799828 * (2216091 - 1 ) + 1
Possible prime factor of the double Mersenne number MM31 (22216091-1-1).
Unfortunately, this prime number of 65,057 digits does not divide MM31.
10th June 2014 (65,057 digits).
2 * 1879484 * (2216091 - 1 ) + 1
Possible prime factor of the double Mersenne number MM31 (22216091-1-1).
Unfortunately, this prime number of 65,057 digits does not divide MM31.
11th June 2014 (65,057 digits).
2 * 9488 * (22976221 - 1 ) + 1
Possible prime factor of the double Mersenne number MM36 (222976221-1-1).
Unfortunately, this prime number of 895,937 digits does not divide MM36.
10th March 2014 (895,937 digits).
2 * 140340 * (21257787 - 1 ) + 1
Possible prime factor of the double Mersenne number MM34 (221257787-1-1).
Unfortunately, this prime number of 378,638 digits does not divide MM34.
10th January 2014 (378,638 digits).
226795 + 57083
Prime digit with no special form, certified and verified with Primo.
22nd November 2009 (8,067 digits).
61876115 * [RSA200]512 - 1
where RSA200 is the 200 - digit RSA factorization challenge number.
4th June 2005 (102,128 digits).
32476090*C(1531785651*210110+18,23)-1
Distributed search for a provable prime of the form p = k*C(x,23)-1 where C is the binomial function. Factoring p+1 to 30.9% and sieving by Jens Kruse Andersen. Proving p+1 factors with Primo by Pierre Cami, Luigi Morelli and V. M. Ulyanov. PRP tests with PrimeForm by the 4 mentioned and Décio Luiz Gazzoni Filho. PRP found by Pierre Cami. Konyagin-Pomerance primality proof by David Broadhurst.
June 2005.
25987968300*[RSA-200]512-1 and 49334180280*[RSA-200]512-1
A distributed search for a prime of the form k*[RSA-200]^512-1 which can only be proven prime by using the factorization of RSA-200, the product of 2 random 100-digit primes. Writing and running sieve to 10^12 by Jens Kruse Andersen. PRP tests by Jens Kruse Andersen, Göran Axelsson, Pierre Cami, Phil Carmody, Chuck Lasher, Predrag Minovic, Luigi Morelli, Martin Speirs, V. M. Ulyanov, Paul Underwood and Cedric Vonck. Finding and proving primes by Luigi Morelli and Paul Underwood.
May 2005.
22055611200*(10999+203959)#/(10999)#-1
A distributed search for a prime on the form p = k*(10999+203959)#/(10999)#-1, where the 101 smallest titanic primes divide p+1. Proving p+1 factors, writing and running sieve to 10^12 by Jens Kruse Andersen. PRP tests by David Broadhurst, Pierre Cami, Phil Carmody, Ken Davis, Predrag Minovic, Luigi Morelli and Paul Underwood. Finding and proving prime by David Broadhurst.
January 2005.
708477982733*3*5*11*13*19*29*37*53*59*2231290+1 (69649 cifre) 27 gennaio 2004 15:53:00 CDT - Payam number
3ˇ 2727699-1 (219060 cifre) 23 gennaio 2004 15:59:21 CDT - 321Search
210885 . 2295335-1 (88911 cifre) 25 novembre 2003 15:36:49 CDT - 15K search
1650292215 ˇ 2140588-1 (42331 cifre) 19 agosto 2003 18:04:12 CDT - 15K search
1650292215 ˇ 2127041-1 (38253 cifre) 19 agosto 2003 18:04:12 CDT - 15K search
1650292215 ˇ 2123255-1 (37113 cifre) 19 agosto 2003 18:04:12 CDT - 15K search
2. Fattorizzazione
(38ˇ10174-11)/9
= 401 ˇ 1531 ˇ 2333 ˇ 11103172231868232665208082632227[32] ˇ C134
C134 = P41 ˇ P93
P41 = 38399983418304274738274024976546740584967[41]
P93 = 727788294601551888099993904173706931765025315072705833126180244134209183779214775385936665507[93]
(Luigi Morelli / GGNFS 0.77.1 + msieve 1.39 for P41 x P93 / Mar 17, 2009 / 134 digits)
(4ˇ10174+41)/9
= 33 ˇ 7629737812981[13] ˇ 31668315658185358241[20] ˇ 64583320974668012969282589628685014327[38] ˇ C104
C104 = P44 ˇ P60
P44 = 13572177173944141379230865642040566250314827[44]
P60 = 738367971619864478723854016085408967268073560203846001125847[60]
(Luigi Morelli / GGNFS 0.77.1 + msieve 1.39 for P44 x P60 / Jan 4, 2009 / 104 digits)
(34ˇ10174-43)/9
= 23279 ˇ 344848243 ˇ 80308935953[11] ˇ 685748829763[12] ˇ 41268157890120643[17] ˇ C123
C123 = P53 . P70
P53 = 20911043547722046862836516832845716851816899295541089[53]
P70 = 9902032167234716303717452177033910330401475786201296097689113927382553[70]
(Luigi Morelli / msieve 1.38 for P53 x P70 / 23.84 hours / Dec 1, 2008 / 123 digits)
c 14535 = 31 . 101 . 599 . 9721 . 21860034500477033057[20] . 5024561734078743614019475672210465536770797634435009651390623763133271404343125421517983291123932203[c100]
c100 = 95615984081251482246538695683308609617345441049 . 52549391007773634411218693704643056941771279438002147
(Luigi Morelli / msieve 1.30 for P47 x P53 / QS / Dec 18, 2004 / 100 digits)
2607-3 = 55 . 19 . 263 . 1401457092703061[16] . 254605005861515627419[21] . 1107375018476949027223897414997873720048902633664994028034804453[77]
p77 # Luigi Morelli and Alexander Kruppa SNFS 16 Dec 2004 - 98 digits.
c 14536 = 34 . 20411 . 9900799 . 194677459885211[15] . 8996108210139462978073236775295867026748488312730764496163714592360959433517967920644604084256992347[c100]
c100 = 866509691540844271532732996709594633227[39] . 6071749876355753270908403958358496758132678092506191524465563[61]
(Luigi Morelli / msieve 1.30 for P39 x P61 / QS / Dec 13, 2004 / 100 digits)
3. Ricerca fattori GFN e xGF (Fermat numbers)
New factors k.2^n + 1 of a^(2^m) + b^(2^m) a b m k n Year Digits ------------------------------------------------------------ 3 1 46352 197909 46353 2011 13,959 5 1 109737 5921 109739 2010 33,039 5 3 48370 129669 48371 2011 14,567 5 3 90011 23559 90013 2013 27,101 5 3 98971 19159 98974 2013 29,799 5 4 93834 12339 93837 2013 28,252 7 2 5671 2004304135 5672 2018 1,717 7 2 14392 28371113 14393 2017 4,341 7 2 46064 163211 46067 2011 13,873 7 6 6413 4828195 6414 2010 1,938 7 6 105719 4491 105720 2010 31,829 8 1 6659 4362423 6661 2010 2,012 8 1 49501 140739 49503 2011 14,908 8 3 109604 2261 109605 2010 32,998 8 3 5671 1755293137 5672 2018 1,717 8 7 5674 1982981535 5675 2018 1,718 9 5 14097 20085603 14098 2017 4,252 9 5 14498 21704897 14499 2017 4,372 9 5 93119 25447 93120 2013 28,036 10 1 71634 13633 71636 2010 21,569 10 3 92482 18357 92483 2013 27,845 10 7 105723 3963 105725 2010 31,830 11 1 6720 9596875 6722 2010 2,031 11 4 107259 2493 107261 2010 32,293 11 6 6658 5922527 6659 2010 2,012 11 7 99621 18551 99627 2013 29,995 11 9 46959 152641 46960 2011 14,142 11 10 5652 2491340445 5654 2018 1,712 12 11 92561 15783 92565 2013 27,870 12 11 105308 4631 105309 2010 31,705 12 11 107583 6699 107590 2010 32,392
4. Ricerca prime gaps
Con prime gap si intende la differenza tra un numero primo ed il successivo.
L'ennesimo prime gap, definito gn o g(pn) è la differenza tra il numero primo (n + 1)-esimo e l' n-esimo.
Il risultato seguente è stato ottenuto attraverso il team PGS (Prime Gap Sequences), organizzato su MersenneForum.
Il team comprende (in stretto ordine alfabetico):
S. Cole, L. Desnogues, R. Gerbicz, D. Jacobsen, A.P. Key, L. Morelli, A. Nair, C.E.L. Pinho, M. Raab, T. Ritschel, R.W. Smith (coordinator), D. Stevens.
I programmi per la ricerca al computer, in C and Perl, sono stati sviluppati da Robert Gerbicz, Dana Jacobsen, Antonio P. Key ed ottimizzati da tutti gli utenti.
La ricerca è iniziata ad aprile 2017 ed è tuttora in corso.
========================================================================================= Gap Cls Discvrer Year Merit Digts Following the prime ========================================================================================= 1450 CFC LMorelli 2017 33.16 19 9808299410025809701