Talk:Pierpont prime

mathematics of paper folding

The information I included comes entirely from this web page. Doesn't seem quite relevant to the article, but it seems useful to record the reference. Hv 03:11, 2 September 2005 (UTC)

Largest known Pierpont prime

Last night, I removed the statement

"As of 2005, the largest known Pierpont prime is 2⁴⁷ 3⁶² + 1 = 53694226297143959644031344050777763036004353, discovered by Walter Nissen."

I did so rather hastily with a terse edit summary, for which I apologize.

However, my removal was reverted with the summary "I'm convinced Nissen discovered it." This may well be true, but in my interpretation of WP:V, we cannot make a claim like this without some corraboration. This is not the most important point for me however. I find it very hard to believe that this is indeed the largest known Pierpont prime. I believe it is not that hard to test 100-digit numbers of this structure for primality. So, I'm intending to remove that sentence again. -- Jitse Niesen (talk) 12:42, 19 October 2005 (UTC)

Thank you for not deleting immediately. Why don't we vote on this? Giftlite 23:32, 19 October 2005 (UTC)

Because we don't vote on everything. The idea is that we first try to reach an agreement between ourselves. If we can't manage that, we try to involve more people, for instance by posting at Wikipedia:WikiProject Mathematics or Wikipedia:Requests for comment/Maths, natural science, and technology. If that all fails, we may do a vote as a last resort. -- Jitse Niesen (talk) 17:21, 20 October 2005 (UTC)

definition

For the condition :

any positive integers u and v

see instead :

http://www.research.att.com/projects/OEIS?Anum=A058383

The condition :

any non-negative integers u and v

would be helpful to some readers , but is also verbose.

Once the subject becomes (rational) primes , then the Fundamental Theorem (= unique factorization) must automatically be incorporated . The Fundamental Theorem is meaningless nonsense outside Z . The question becomes: "How often do you want to say 'integer' ?". In every definition relating to (rational) primes ? Walter Nissen 2005-10-23 19:09 UTC

Yes, the OEIS indeed supports you. However, changing the definition does have knock-on effect: the sequence of Pierpont primes must be changed (I did this now), and I guess the largest known Pierpont prime under this definition is actually the largest known prime. Is that article up-to-date? -- Jitse Niesen (talk) 21:14, 23 October 2005 (UTC)

According to the D. A. Cox & J. Shurman and Andrew M. Gleason

articles cited at :

http://www.research.att.com/projects/OEIS?Anum=A005109

greater than 3 is part of the definition .

The Mersennes are 2^p - 1 ; the Fermats are 2^2^n + 1 ; the
Pierponts are 2^u*3^v + 1 .
Find an n > 4 and you'll be famous .

In the statement :

If p is a Pierpont prime, v=0, and u=2^n , we have a Fermat prime.

u = 2^n is properly part of the conclusion(!) , not part of the hypothesis . Also , p is already a Pierpont prime .

Thus :

If v=0, then u=2^n and we have a Fermat prime.

Walter Nissen 2005-10-25 01:43 UTC
( note use of ISO 8601-compliant time format . )

Our article requires p>3, but the references http://www.research.att.com/~njas/sequences/A005109 and http://mathworld.wolfram.com/PierpontPrime.html both include p=2 and p=3. We should either change the definition or add a good reference to our definition (and probably also mention that the other definition exists). PrimeHunter (talk) 14:57, 6 March 2008 (UTC)

Who's Pierpont??

The first sentence should read thus:

A Pierpont prime, named after XXXX Pierpont, is a prime number greater than 3 having the form

$2^{u}3^{v}+1\,$

for some integers u,v ≥ 0.

Michael Hardy 19:29, 21 November 2005 (UTC)

Add a reference to the Huzita-Justin Axioms

Add a reference to the Huzita-Justin Axioms:

Using the six (or seven) Huzita axioms, it is possible to: Construct a regular N-gon for N of the form 2^i 3^j (2^k 3^l + 1) when the last term in parentheses is a prime (a so-called Pierpont Prime);

http://www.langorigami.com/science/math/hja/hja.php