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 2014-03-30, 09:42 #2 Brian-E     "Brian" Jul 2007 The Netherlands 2·3·5·109 Posts Is the conjecture merely motivated by observation that it works for small p and the probability that two of the conditions (let alone three) are satisfied very quickly becomes vanishingly small? (And hence the conjecture is expected to hold in rather the same way that the conjecture of no Fermat primes beyond F4 is expected.) Or is it in fact conjectured that there are more occurrences of all three conditions holding beyond the last known case of p=127? Last fiddled with by Brian-E on 2014-03-30 at 09:43
2014-03-30, 12:48   #3
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

1D2416 Posts

Quote:
 Originally Posted by Brian-E Is the conjecture merely motivated by observation that it works for small p and the probability that two of the conditions (let alone three) are satisfied very quickly becomes vanishingly small?
Yes. Furthermore, John indicated that he was not really serious
when he proposed it.

This "conjecture" is basically a joke.

 2014-03-30, 14:24 #4 axn     Jun 2003 537410 Posts I always thought that NMC was inspired by Mersenne's original conjecture list 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, which indeed picks out primes of the form 2^k+/-1 and 4^k+/-3 (except 61, which, while of the form 4^k-3 and in fact gives a Mersenne prime, was left out by Mersenne). Could be a coincidence though.
2014-03-30, 21:31   #5
ewmayer
2ω=0

Sep 2002
República de California

5×2,347 Posts

Quote:
 Originally Posted by axn I always thought that NMC was inspired by Mersenne's original conjecture list 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, which indeed picks out primes of the form 2^k+/-1 and 4^k+/-3 (except 61, which, while of the form 4^k-3 and in fact gives a Mersenne prime, was left out by Mersenne). Could be a coincidence though.
One good joke deserves another.

2014-03-31, 01:15   #6
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by ewmayer One good joke deserves another.
Can we test the validity of it in this thread ? There's a pattern in the difference between (2^(2n+1) + 1)/3 and the next Mersenne number. Basically, A080674 with an extra 0 on the front. Could we test the validity of it based on this ? Admittedly, I have a portfolio to complete for school, so I might get around to it myself.

2014-03-31, 13:45   #7
CRGreathouse

Aug 2006

175B16 Posts

Quote:
 Originally Posted by R.D. Silverman This "conjecture" is basically a joke.
Yes. It seems to be an example of a theorem which is true by coincidence. (I would love to be proved wrong here!)

Last fiddled with by CRGreathouse on 2014-03-31 at 13:45

2014-03-31, 21:27   #8
Kathegetes

Jul 2012
Paris, France.

6316 Posts
Hello ewmeyer I do not get here often, but I recall a reason to respect you

Quote:
 Originally Posted by ewmayer One good joke deserves another.
Some think, weight givens, speak without reaching conclusion missing some step. Given; more can be known than is capable of being penetrated by mere mortal logic at some moment. I may have read Mersenne's list may be uncertain in regards to 61 or 67 ie, reading his hand writing. If you please to confirm the following... your friends may be pleased to wager conjectures entrusting all to TIME ; as she alone has proven herself a noble guardian of all entrusted unto her, whether mortal or divine. On the quantity of members of ( S ) less than a given term of G. Let K be a known prime such that 2^K-1 is prime D, such that D(D+1)/2 is some S, sum of her parts. Let G0= triangular radix of 8 = 3.5311... Zero S less than G0. G1=8, G2=36, G3=666, all terms of G follow by triangulation of 8. The members of S show an increase. Present knowledge of proper order of S being incomplete though perhaps correct up to G28. At G30 we delight in desire to know. K.D.S projects merely 53 as a divine statement. All such being feminine intuitive conjectures divined in TIME. When will 5 be proven in any term? Then 6,7,8...should mortals divine no logic in such trivial beauties?

2014-03-31, 22:49   #9
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

22·5·373 Posts

Quote:
 Originally Posted by Kathegetes Some think, weight givens, speak without reaching conclusion missing some step. Given; more can be known than is capable of being penetrated by mere mortal logic at some moment. I may have read Mersenne's list may be uncertain in regards to 61 or 67 ie, reading his hand writing. If you please to confirm the following... your friends may be pleased to wager conjectures entrusting all to TIME ; as she alone has proven herself a noble guardian of all entrusted unto her, whether mortal or divine. On the quantity of members of ( S ) less than a given term of G. Let K be a known prime such that 2^K-1 is prime D, such that D(D+1)/2 is some S, sum of her parts. Let G0= triangular radix of 8 = 3.5311... Zero S less than G0. G1=8, G2=36, G3=666, all terms of G follow by triangulation of 8. The members of S show an increase. Present knowledge of proper order of S being incomplete though perhaps correct up to G28. At G30 we delight in desire to know. K.D.S projects merely 53 as a divine statement. All such being feminine intuitive conjectures divined in TIME. When will 5 be proven in any term? Then 6,7,8...should mortals divine no logic in such trivial beauties?

What kind of drugs are you taking?

2014-04-01, 00:46   #10
NBtarheel_33

"Nathan"
Jul 2008
Maryland, USA

5·223 Posts

Quote:
 Originally Posted by R.D. Silverman What kind of drugs are you taking?
Or perhaps (of the psychotropic variety) *not* taking?

2014-04-01, 04:19   #11
TheMawn

May 2013
East. Always East.

11·157 Posts

Quote:
 Originally Posted by NBtarheel_33 Or perhaps (of the psychotropic variety) *not* taking?
I must be not taking the same drugs. I couldn't even follow it.

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