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 2006-02-14, 12:54 #1 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 22·33·19 Posts Alternative Test for Primes. Alternative Test for Primes. I quote from TAOCOP by Donald E. Knuth. “The worlds largest explicitly known primes have always been Mersenne primes. But the situation might change since M/Primes are getting harder to find” Testing numbers of the form N =5.2^n + 1 for primality with the same number of squarings mod N as the LL test should be a feasible alternative. Mally
2006-02-14, 13:08   #2
rogue

"Mark"
Apr 2003
Between here and the

3·19·113 Posts

Quote:
 Originally Posted by mfgoode Alternative Test for Primes. I quote from TAOCOP by Donald E. Knuth. “The worlds largest explicitly known primes have always been Mersenne primes. But the situation might change since M/Primes are getting harder to find” Testing numbers of the form N =5.2^n + 1 for primality with the same number of squarings mod N as the LL test should be a feasible alternative. Mally

2006-02-14, 13:16   #3
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

40048 Posts
Alternative Test for Primes

Quote:
 Originally Posted by rogue Already being tested at http://www.prothsearch.net
Correct me if Im wrong but the numbers I have given are are +1 not -1. I confess Im not much into this type.
Mally

2006-02-14, 15:27   #4
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22·33·19 Posts
Alternate Test for Primes

Quote:
 Originally Posted by mfgoode Correct me if Im wrong but the numbers I have given are are +1 not -1. I confess Im not much into this type. Mally
:surprised Sorry I took a cursory check on the URL before I posted. A second check gave me the answer. Well I learnt something on Proth Primes.
Mally

 2006-02-16, 17:00 #5 Greenbank     Jul 2005 18216 Posts If you look at: http://primes.utm.edu/largest.html you'll notice the top 5 primes are Mersenne (M43? to M39?), and 4 of the remaining 5 are Proth primes. The 8th largest known prime is M38.
 2006-02-16, 18:02 #6 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 22×33×19 Posts Alternate Test for Primes Thank you Greenbank for this valuable information. I presume there are still unknown primes between the ones listed. Mally
2006-02-16, 20:09   #7
xilman
Bamboozled!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

97×113 Posts

Quote:
 Originally Posted by mfgoode Thank you Greenbank for this valuable information. I presume there are still unknown primes between the ones listed. Mally
Don't be silly.

The number of primes less than N is about N/logN. Where are you going to fit all the primes smaller than the largest known prime? The number of such primes is itself vastly greater than the second-largest known prime.

Paul

 2006-02-16, 23:27 #8 garo     Aug 2002 Termonfeckin, IE 1010110011002 Posts Come come now Paul. The showed that mally was well aware of that. Or was he?
2006-02-19, 16:25   #9
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22×33×19 Posts
Alternative Test for Primes

Quote:
 Originally Posted by garo Come come now Paul. The showed that mally was well aware of that. Or was he?
Thank you Garo. Of late, Paul is indulging in reading a different meaning
in straight forward posts . He enters into a labyrinth of ideas and knots himself up. You know Festus' assessment of Paul (The apostle)"much-- learning has......"
Mally

 2006-02-28, 09:30 #10 yucell     Feb 2006 İSTANBUL 5 Posts (2^k)+1=prime???? k for 2=5 k for 4=17 k for 16=65537 k for 256=............ k for 65536=............. k for 4294967296=............... can it be?
 2006-02-28, 11:53 #11 Greenbank     Jul 2005 2·193 Posts Again, No. 2^256+1 has a factor 1238926361552897.

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