Good projects never die, they simply reserve the right to take a rest every so often. However, I, and others, think the factorial prime seach has rested quite...
17116
ed pegg
xeipon2
Nov 1, 2005 5:58 pm
Is the following true? For any number n with less than 20000 digits, if n+1 or n-1 is an easily factorable smooth number, then the primality/non-primality of n...
17117
Jonathan A. Zylstra
jonzylstra2000
Nov 1, 2005 6:49 pm
... The Prime Pages contain all sorts of useful knowledge about prime numbers. For your question, yes, it's true, it can be established with certainty, and...
17118
Hugo Scolnik (fiber)
scolnik2003
Nov 1, 2005 7:41 pm
Dear all: I have posted the question appearing below and there was no single answer. Best Hugo Scolnik A programming language is low level when its programs...
17119
Jens Kruse Andersen
jkand71
Nov 1, 2005 7:44 pm
... If you want old contents of a URL then try the Internet Archive: http://www.archive.org http://web.archive.org/web/20040922151554/http://powersum.dhis.org/...
17120
Ignacio Larrosa Ca...
ilarrosa
Nov 1, 2005 8:12 pm
Tuesday, November 01, 2005 8:40 PM [GMT+1=CET], ... Hugo, If t = 0 (mod 11), a + b*t can't be multiple of 11, but in other case yes. By example, for t = 10, a...
17121
Jens Kruse Andersen
jkand71
Nov 1, 2005 8:35 pm
... Yes, this and more is true. Any number n can be proven prime/composite "easily", in time O(d^2 * log d * log log d) where d = log n, _if_ enough of the...
17122
gordon_as_number
gordon_as_nu...
Nov 1, 2005 9:08 pm
The paper located at xxx.arXiv.org/physics/0503159 answers your question. Regards, Gordon physics/0503159 [abs, ps, pdf, other] : Title: Fast Factoring of...
17123
elevensmooth
Nov 1, 2005 9:54 pm
... answer. Dear Hugo, Please see message 17083, where I explained why your satement about "no squares" was wrong, gave a generic formula for generating an ...
17124
theo2357
Nov 2, 2005 5:44 pm
Let p,q,r be three consecutive primes. How can be proven that 1/p < 1/q + 1/r? It's NOT trivial!...
17125
Jose Ramón Brox
ambroxius
Nov 2, 2005 11:17 pm
... From: "theo2357"; <Theo.3.1415@...> Let p,q,r be three consecutive primes. How can be proven that 1/p < 1/q + 1/r? It's NOT trivial! ...
17126
Wojciech.Florek@...
wsflorek
Nov 2, 2005 11:20 pm
... This is equivalent to a statment that for a given prime q the preceding prime p>=2q/3. Supose it is true. Moreover, it is evident (and there is threom...
17127
Jose Ramón Brox
ambroxius
Nov 2, 2005 11:33 pm
... From: "Jose Ramón Brox" <ambroxius@...> q/p < 3/2 is a simpler necessary condition that seems to hold if p>7. ... I mean it's a SUFFICIENT condition....
17128
Milton Brown
miltbrown@...
Nov 3, 2005 6:33 am
Actually, it doesn't seem that hard: 1/p < 1/q + 1/r q>=p+2 r>=q+2>=p+4 It must be shown that 1/p < 1/(p+2) + 1/(p+4) equivalently (p+2)(p+4)/p < 2p +6 or ...
17129
Jose Ramón Brox
ambroxius
Nov 3, 2005 8:57 am
... From: "Milton Brown" <miltbrown@...> Actually, it doesn't seem that hard: 1/p < 1/q + 1/r q>=p+2 r>=q+2>=p+4 It must be shown that 1/p < 1/(p+2)...
17130
Jan van Oort
sanctushilarius
Nov 3, 2005 11:12 am
... From: Jan van Oort <glorifier@...> Date: Nov 3, 2005 12:10 PM Subject: Re: [PrimeNumbers] reciprocal consecutive primes To: theo2357...
17131
Jose Ramón Brox
ambroxius
Nov 3, 2005 12:00 pm
... From: "Jan van Oort" <glorifier@...> p^2 > mn which is true iff ( m < p AND n < p ) OR ( m = p + a AND n = p - b AND b > a ) ( condition i ) ... ...
17132
Jose Ramón Brox
ambroxius
Nov 3, 2005 12:03 pm
... From: "Jose Ramón Brox" <ambroxius@...> Consider b = a-1, then we have m*n = (p+a)(p-b) = (p+a)(p-a+1) = p^2 +p-a(a+1) ... The final equality should...
17133
Jeremy Wood
mickleness
Nov 3, 2005 4:38 pm
Gauss-Legendre conjectured that the prime counting function of x is similar to x/ln(x). (Or more specifically that as x approaches infinity: pi(x)/(x/ln(x)) ->...
17134
theo2357
Nov 3, 2005 5:07 pm
I don't know if it's proven. It's my own observation. 1/p < 1/q + 1/r is equivalent to: p > qr/(q+r) which means p is greater than the half of the harmonic ...
17135
theo2357
Nov 3, 2005 5:26 pm
Gauss: pi(x) ~ x/ln x Legendre: pi(x) ~ x/(ln x – 1,08366) Today : pi(x) ~ x/(ln x - 1)...
17136
theo2357
Nov 3, 2005 5:29 pm
Gauss: x/ln x Legendre: x/(ln x – 1,08366) Today : x/(ln x -1)...
Can anyone sieve the form N= (2^k)*(2^(k+1) + 1) + 1? Mark R., can you customize Multisieve? Phil C., can you customize ksieve? Can anyone else customize a...
17139
jbrennen
Nov 3, 2005 10:20 pm
... I think this is implied by the Iwaniec & Pintz finding, namely that there is always a prime between x and x-x^(23/42), for any real number x > 11. The...
17140
Hugo Scolnik (fiber)
scolnik2003
Nov 3, 2005 11:09 pm
I am studying under what cinditions a expression of the form a + b*t generates perfect squares and when those can be written by a number of quadratic...
17141
Mark Rodenkirch
mgrogue
Nov 4, 2005 12:09 am
... Sorry, I have little time to spend on this. --Mark...
17142
Paul Underwood
paulunderwooduk
Nov 4, 2005 12:19 am
... Phil Carmody not only has a sieve for this form, he also has a PRP test program that is quicker than PFGW for this form. Good luck! Paul...
17143
zarei176
Nov 4, 2005 6:21 am
hi guys what is euler's proof for fermat's theorem? whose is said:if p a prime number then p divide a^p-1 -1...
17144
Dario Alpern
alpertron
Nov 4, 2005 8:12 pm
... b*t generates perfect squares and when those can be written by a number of quadratic polynomials (obviously a must be a quadratic residue of b) ... ...
