10^12000+3213 is a probable prime. By the way these numbers prove that P =/ NP. Primes are in NP (Pratt, 1975). But, primes are not decidable in polynomial...
Milton Brown
miltbrown@...
Mar 29, 2001 9:35 pm
... I have refrained from commenting on P versus NP, thus far. My understanding is restricted to some parts of Stephen Cook's precise formulation of the $1M ...
d.broadhurst@...
Mar 29, 2001 10:58 pm
... Don't forget what your statement means. If primality proving cannot be in P, Riemann's Hypothesis is false. -- Barubary...
Barubary
barubary@...
Mar 29, 2001 11:04 pm
... Thanks for the reminder! I was talking to Alain Connes recently and told him: "If you manage to prove GRH, it will transform primality proving, in the...
d.broadhurst@...
Mar 29, 2001 11:55 pm
I'm not a mathematician, nor do I know much about Riemann's Hypothesis (how Zeta() can have zeros at all is a mystery to me :) ). What I do know is that...
Barubary
barubary@...
Mar 30, 2001 2:03 am
... I meant a non-deterministic polynomial bound, almost always, as in ECPP. (And I should have said so, sorry, since being in NP is something different, as...
d.broadhurst@...
Mar 30, 2001 3:24 am
Yes, I have read Cook's proof....
Milton Brown
miltbrown@...
Mar 30, 2001 2:36 am
... No you haven't, Milton, because there is no proof. Cook is justly famous for formulating a question that no-one has yet answered. That's why he was asked...
d.broadhurst@...
Mar 30, 2001 2:58 am
What exactly is wrong? So, Riemann was wrong for once, it has happened to the best of us. Milton L. Brown...
Milton Brown
miltbrown@...
Mar 30, 2001 2:41 am
... Also, I don't think any knowledgeable person thinks that the ERH is false. If the ERH is true then primes are in P. ...
Jud McCranie
jud.mccranie@...
Mar 30, 2001 3:08 am
Sorry, I thought you meant the proof of the Cook-Levinson Theorem. Milton...
Milton Brown
miltbrown@...
Mar 30, 2001 4:06 am
... Sorry, I don't know that theorem. Norman Levinson did many fine things, such as his work on the zeros of the Riemann zeta function and his famous letter to...
d.broadhurst@...
Mar 30, 2001 5:31 am
How specifically is it wrong? Could you define "knowledgeable person"? Or is that wrong, too?...
Milton Brown
miltbrown@...
Mar 30, 2001 4:09 am
... You're stating this without any proof or evidence: "But, primes are not decidable in polynomial time, example of this number and infinitely many others. ...
Jud McCranie
jud.mccranie@...
Mar 30, 2001 4:39 am
David, The reason I was confused seems to be your statemnt: "Anyone who thinks that is is easy to decide whether P is or is not the same as NP should read...
Milton Brown
miltbrown@...
Mar 30, 2001 5:30 am
... History is always moot. Jack Edmonds paper on matroids was clearly influential, as Cook says in the Clay 2000 PDF formulation to which I directed you. ... ...
d.broadhurst@...
Mar 30, 2001 5:41 am
... Milton's right this time. Cook came up with NP-completeness. +--------------------------------------------------------+ ... ...
Jud McCranie
jud.mccranie@...
Mar 30, 2001 8:24 pm
... Thanks, Jud. I uncritically accepted the final sentence of http://www.claymath.org/prizeproblems/pvsnp.htm "Stephen Cook formulated the P versus NP problem...
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