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

[QUOTE=devarajkandadai;109732]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[/QUOTE]
I must first thank Maxal for giving me the training to write the above mini-program(To be contd)

Loud thinking on iregular primes
 

[QUOTE=devarajkandadai;109785]I must first thank Maxal for giving me the training to write the above mini-program(To be contd)[/QUOTE]
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

Loud Thinking on Irregular primes
 

[QUOTE=devarajkandadai;109895]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[/QUOTE]

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

Loud Thinking on irregular primes
 

[QUOTE=devarajkandadai;109895]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[/QUOTE]
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