Re: In the Indirect only W+1 is a prime candidate #28; 2nd ed; Euclid's Infinitude of Primes Proof corrected
1 > I Am
> On 31 Aug, 13:24, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>
> > just tell us what is wrong with a proof that says:
>
> > every number has a prime factorisation (true)
>
> Every integer greater than 1 has a prime factorization.
>
> > therefore W+1 has a prime factorisation (true)
> > take any prime from this factorisation (can be done)
>
> How do you know what its prime fcatorization is ?
>
> > it is not in the given set of primes, and that is a contradiction.
>
> All you know is that no prime from the given set of primes
> divides w+1. This is the contradiction.
proof:
The P versus NP Problem
1. denoted L(M), has associated alphabet Σ and is defined by. L(M) = {w
Σ | M accepts w} Given an integer b > 1, the smallest prime divisor of
b can be
http://www.claymath.org/millennium/P_vs_NP/Official_Problem_Description.pdf
Citations: Every prime has a succinct certificate - Pratt
(ResearchIndex)
V.R. Pratt. Every prime has a succinct certificate. SIAM Journal on
Computing, 4p Gamma1 q i 6j 1 mod p, for all i t 4. C(q i ; w i ) for
all i t. The NP
http://citeseer.ist.psu.edu/context/39245/0
THE P VERSUS NP PROBLEM
THE P VERSUS NP PROBLEM. STEPHEN COOK. 1. Statement of each string w
in Σ Given an integer b > 1, the smallest prime divisor of b can be
found with
http://www.claymath.org/millennium/P_vs_NP/pvsnp.pdf
ALIGNING BRUMER–STARK ELEMENTS INTO A HECKE CHARACTER (WORKING PAPER)
integer dividing W. F . For a prime ideal p of F that does. not divide
W Definition 1. A prime ideal p Spl(K) is Q-orientable if p = Np is odd
and (p 1)/W
http://www.math.umass.edu/~dhayes/Bshecke.pdf
Quantum NP
1. Models of computation. 2. Classical complexity classes P and NP. 3.
NP 1. n , n > 0}. • The alphabet: Σ = {0, 1} The language: L = {w Σ |w
is prime}
http://www.cs.technion.ac.il/~qip-lab/seminar/QNP_I.pdf
[TROFF]
P The general knapsack problem is known to be $NP$-complete [13], and
so it is ( p sup h )$ be a finite field such that $p sup h -1$ has
only moderate prime
http://www.dtc.umn.edu/~odlyzko/doc/arch/knapsack.survey.troff
The Complexity of Some Problems in Cryptography
1 mod p ( prime divisors q of p 1) Corollary 3 (Pratt's Theorem). P
RIM ES NP coNP the machine accepts input w: P r[M accepts w] = b is an
accepting branch
http://acc6.its.brooklyn.cuny.edu/~rbharpaz/ComplexCrypt.pdf
Circuit Complexity
(w) = 1. where n is the length of w. 1. B is in P, and. 2. every A in
P is log space PRIME NUMBER is in NP, and PRIME NUMBER belongs to.
coNP. 24
http://www.compapp.dcu.ie/~wuhai/week11-2003.pdf
VARIATION OF P -ADIC NEWTON POLYGONS FOR L-FUNCTIONS OF EXPONENTIAL
SUMS
zeros are always 1 for each prime ℓ = p. Thus, there remains the; the
weight w(u) is large p, NP(f mod P ) depends only on p and not on the
choice of
http://www.math.uci.edu/~dwan/newton1.pdf
Q.E.D.
Martin M. M. -usatov