20060214, 12:54  #1 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·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 
20060214, 13:08  #2  
"Mark"
Apr 2003
Between here and the
3·19·113 Posts 
Quote:


20060214, 13:16  #3  
Bronze Medalist
Jan 2004
Mumbai,India
4004_{8} Posts 
Alternative Test for Primes
Quote:
Mally 

20060214, 15:27  #4  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Alternate Test for Primes
Quote:
Mally 

20060216, 17:00  #5 
Jul 2005
182_{16} 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.

20060216, 18:02  #6 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×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 
20060216, 20:09  #7  
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
97×113 Posts 
Quote:
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 secondlargest known prime. Paul 

20060216, 23:27  #8 
Aug 2002
Termonfeckin, IE
101011001100_{2} Posts 
Come come now Paul. The showed that mally was well aware of that. Or was he?

20060219, 16:25  #9  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts 
Alternative Test for Primes
Quote:
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 

20060228, 09:30  #10 
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? 
20060228, 11:53  #11 
Jul 2005
2·193 Posts 
Again, No.
2^256+1 has a factor 1238926361552897. 
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