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 2007-07-06, 06:51 #1 devarajkandadai     May 2004 13C16 Posts Loud thinking on irregular primes The relevant numerator of an irregular prime which IS NOT a Mangammal prime has the form 3^n-2.This can easily be identified, on pari, by {p(n)=(3^n-2)/p'} where p' stands for irregular prime which is not a Mangammal prime.The required number is the only integer when we print p(n) for n=1,p'-1. Further observations to be continued. A.K.Devaraj
2007-07-07, 05:12   #2

May 2004

1001111002 Posts

Quote:
 Originally Posted by devarajkandadai The relevant numerator of an irregular prime which IS NOT a Mangammal prime has the form 3^n-2.This can easily be identified, on pari, by {p(n)=(3^n-2)/p'} where p' stands for irregular prime which is not a Mangammal prime.The required number is the only integer when we print p(n) for n=1,p'-1. Further observations to be continued. A.K.Devaraj
I must first thank Maxal for giving me the training to write the above mini-program(To be contd)

2007-07-09, 04:00   #3

May 2004

1001111002 Posts
Loud thinking on iregular primes

Quote:
 Originally Posted by devarajkandadai I must first thank Maxal for giving me the training to write the above mini-program(To be contd)
Secondly I am happy that I could find atleast an indirect aplication of Mangammal primes.
What can we say about the numerator of Bernoulli numbers involving
iMangammal-irregular primes?Its shape is neither 2^n-1 nor that of 3^n-2.
I will revert to this later,
A.K.Devaraj

2007-07-19, 05:45   #4

May 2004

22×79 Posts
Loud Thinking on Irregular primes

Quote:
 Originally Posted by devarajkandadai Secondly I am happy that I could find atleast an indirect aplication of Mangammal primes. What can we say about the numerator of Bernoulli numbers involving iMangammal-irregular primes?Its shape is neither 2^n-1 nor that of 3^n-2. I will revert to this later, A.K.Devaraj
B_20 (-174611) seems to be one such i.e. with shape (3^n-2).In other words the numerator consists of Mangammal-Irregular primes.
A.K.Devaraj

2007-07-25, 03:01   #5

May 2004

4748 Posts
Loud Thinking on irregular primes

Quote:
 Originally Posted by devarajkandadai Secondly I am happy that I could find atleast an indirect aplication of Mangammal primes. What can we say about the numerator of Bernoulli numbers involving iMangammal-irregular primes?Its shape is neither 2^n-1 nor that of 3^n-2. I will revert to this later, A.K.Devaraj
In studying the possible and impossible structure of the numerator of
Bernoulli numbers we come across Mangammal composites (A 119691-OEIS).The numerator of Bernoulli numbers does not permit irregular Mangammal composites.
A.K.Devaraj

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