using 3 and -2 instead of 2 as in 3^n-2
 

Being a novice to Gimps and Maths I was wondering if someone has compiled a series of prime numbers using other bases rather than the classical 2 by Mersenne thereby generating an enhanced list of primes not necessarily Mersenne Prime.
The introduction to Gimps certainly makes one aware of one's abysmal state of ignorance.

People have searched primes in thousands of sequences but more resources are used on Mersenne primes 2^p-1 than any other form. Lists of primes and probable primes of different forms are stored in many different places. For 3^n-2, see [url]http://akpublic.research.att.com/~njas/sequences/A014224[/url] and [url]http://www.primenumbers.net/prptop/searchform.php?form=3%5Ex-2[/url].
Note that many of these numbers are currently only [URL="http://primes.utm.edu/glossary/page.php?sort=PRP"]probable primes [/URL] because it's hard to prove primality of large numbers when most of the prime factorization of the number plus and minus 1 is unknown.

[quote=godot;141195]Being a novice to Gimps and Maths I was wondering if someone has compiled a series of prime numbers using other bases rather than the classical 2 by Mersenne thereby generating an enhanced list of primes not necessarily Mersenne Prime.[/quote]Here's one of the best websites with a wide range of novice-level to expert-level info and lots of links to other primes websites:

"The Prime Pages (prime number research, records and resources)"

[URL]http://primes.utm.edu/[/URL]

using 3 and -2 instead of 2
 

Many thanks for the information you so generously provided in your reply to my post.
The literature is immense and I should be able to gather some ideas ( if only on a superficial level) from a reading of some of it.

To conclude, is Fermat's Little Theorem and Mersenne's formula the first of a class "a^p -(1 or 2)" where "a" and "p" are both prime. If so does this lead to an infinite number of primes.

godot.

[SIZE=3][FONT=Times New Roman]Many thanks for the information you posted in reply to my query.
I should be able to gather a few ideas from the site.

Being of a generation and profession where an Abacus white hot, you can imagine what a culture shock reading about Primes has turned out to be.

Thanks for opening my eyes.


Godot.
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[QUOTE=Jens K Andersen;141199]People have searched primes in thousands of sequences but more resources are used on Mersenne primes 2^p-1 than any other form. .[/QUOTE]


And for very good reason. The LL test is more efficient than any other known
test.....

[QUOTE=godot;141325]

To conclude, is Fermat's Little Theorem and Mersenne's formula the first of a class "a^p -(1 or 2)" where "a" and "p" are both prime. If so does this lead to an infinite number of primes.

godot.[/QUOTE]

This is gibberish.

gibberish
 

[FONT=Times New Roman][SIZE=3]R D Silverman described a throw away comment in a thank you letter by me to Jens K Andersen as gibberish.

Of course it is gibberish.
How else does one learn except by asking stupid questions?

Both Jens K Andersen and Cheesehead took the time and effort to reply to my original post. Their assistance was greatly appreciated and has provided me with an amazing collection of interesting references. I politely thanked both of them for their contributions.

As I freely admitted in my first post I was a novice. In fact you will realise that I still do not know how to post correctly, however I shall learn.

Regarding the response to my throw away comment about a class of Primes by R D Silverman, it seems to me that it was a waste of time as he was only stating the obvious. I am sure that most members of the Forum, had they read it, would have dismissed it out of hand.
Were I in the omniscient position in the study of Maths that R D Silverman is, I am sure I could find a more productive use of my time than making derogatory comments on foolish asides by a novice.

Godot.
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[QUOTE=godot;141518][FONT=Times New Roman][SIZE=3]R D Silverman described a throw away comment in a thank you letter by me to Jens K Andersen as gibberish.

Of course it is gibberish.
How else does one learn except by asking stupid questions?


[/SIZE][/FONT][/QUOTE]

The issue isn't that the question was mathematically stupid.
The issue is that the language used to pose the question made no sense.
This isn't a mathematical issue.

I assume that if one is interested in a problem, that one will at least
take the time to pose a question that makes sense, even if the math is
wrong.

[QUOTE=godot;141325]To conclude, is Fermat's Little Theorem and Mersenne's formula the first of a class "a^p -(1 or 2)" where "a" and "p" are both prime. If so does this lead to an infinite number of primes.[/QUOTE]
FWIW, a[sup]p[/sup]-1 for any prime a != 2 is an even number and therefore not prime.

[quote=drew;141894]FWIW, a[sup]p[/sup]-1 for any prime a != 2 is an even number and therefore not prime.[/quote]I suspect that godot's "a^p -(1 or 2)" meant to subtract the appropriate choice of 1 (for even a) or 2 (for odd a).

- -

godot,

Clearer would be stating two separate cases -- for example: "... classes 'a^p - 1' (for even prime a) and 'a^p - 2' (for odd prime a), where p is also prime."

Since 2 is the only even prime, so that the first class has only the (exceedingly well-known, on this forum) single member "2^p - 1", most folks would rather that you'd just mentioned the second of those two classes, I think. (Also, your thread title is about the latter.)