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Old 2007-07-06, 06:51   #1
devarajkandadai
 
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May 2004

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Default 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
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Old 2007-07-07, 05:12   #2
devarajkandadai
 
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Default

Quote:
Originally Posted by devarajkandadai View Post
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)
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Old 2007-07-09, 04:00   #3
devarajkandadai
 
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Default Loud thinking on iregular primes

Quote:
Originally Posted by devarajkandadai View Post
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
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Old 2007-07-19, 05:45   #4
devarajkandadai
 
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Default Loud Thinking on Irregular primes

Quote:
Originally Posted by devarajkandadai View Post
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
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Old 2007-07-25, 03:01   #5
devarajkandadai
 
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Default Loud Thinking on irregular primes

Quote:
Originally Posted by devarajkandadai View Post
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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