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-   -   Loud thinking on irregular primes (https://www.mersenneforum.org/showthread.php?t=8607)

devarajkandadai 2007-07-06 06:51

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

devarajkandadai 2007-07-07 05:12

[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)

devarajkandadai 2007-07-09 04:00

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

devarajkandadai 2007-07-19 05:45

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

devarajkandadai 2007-07-25 03:01

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


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