a := sum ({n,1,k}, prime_n^(1/n) – prime_(n+1)^(1/(n+1))) ,  {n,1,k} means n=1 to k. For k <= 1,000,000, observe a < 1, and a-->1.  What is the largest...
I do not know why the extra characters were place in, but here it is again. a := sum ({n,1,k}, prime_n^(1/n) – prime_(n+1)^(1/(n+1))) , {n,1,k} means n=1 to...
... which was an unhelpful way of defining a(k) = 2 - prime(k+1)^(1/(k+1)) At large k, the PNT gives (1 - a(k))*log(k)/k = 1 + O(log(log(k))/log(k)) David...
I have a couple undergraduate students researching the history of the primality of one. For example, most of the early Greeks did not consider one to be a...
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Walter Nissen
nissen@...
Feb 2, 2012 8:41 pm
A most interesting subject . I think the most accessible definition of prime is geometrical , rectangularization forces linearization , ...
phi(1) has to equal 1 in order to preserve the multiplicative nature of phi(). In other words, If gcd(a,b) == 1, then phi(a)*phi(b)==phi(a*b). 1 is the only...
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Paul Leyland
paul@...
Feb 3, 2012 12:22 pm
... To the Pythagoreans, primality and irrationality were closely related ... Although odd by modern standards, it arose from their fundamentally geometric...
... But then some Germans disagreed, circa 1900: http://www.peterhug.ch/lexikon/primzahl/13_0390 http://de.academic.ru/dic.nsf/meyers/111736 Des goûts et des...
... V. A. Lebesgue designated 1 as prime on page 5 of his 1859 textbook: http://books.google.co.uk/books?id=ea8WAAAAQAAJ He is not to be confused with Henri...
... Fundamental, pervasive, and perverted. It is, after all, a language in which the singular 'thou' has been jetisoned for the plural 'you', and similarly the...
... Is/are Manchester ******* United singular/plural? Meanwhile, back in the archives: on page 252 of http://www.gutenberg.org/ebooks/31246.html Rouse Ball...
We say that primes must have only 2 divisors. In other hand, if number has 2 divisors, it's prime. 2 is also prime and the first element and only even element...
Mensaje marcado sábado, 4 de febrero de 2012 10:23 La unidad no es primo porque tiene dos divisores en vez de cuatro; ademas, si lo fuera, seria invalido EL...
... Dr. Casaubon, I hope you see that your definition as you state it doesn't clarify things. Of which primes is 1 the product? Either your statement of the ...
front page of NY Times just featured this paper http://eprint.iacr.org/2012/064.pdf which is hilarious! Just when you thought you'd seen the ultimate in human...
... "among the 4.7 million distinct 1024-bit RSA moduli that we had originally collected, more than 12500 have a single prime factor in common" Hint to...
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Paul Leyland
paul@...
Feb 15, 2012 10:15 am
... Easier said than done. First, you have to get Arjen's database. Once you have it, finding factors through GCDs is a non-trivial task. That is the limit...
... Presumably you get it from the same places that Arjen got it? ... I think I can do it in about the cost of about a dozen half-gigabyte GCDs. Looking at...
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Paul Leyland
paul@...
Feb 15, 2012 5:06 pm
... That's one way. It's also consistent with my statement that it's easier said than done. ... If you think you can do it, you can easily verify whether you...
... R[SA] is not keen on D[H], but more relaxed about D[VW]: http://www.rsa.com/rsalabs/node.asp?id=2248 ... or Station-to-Station (STS) protocol, was...
... https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0503&L=nmbrthry&P=R684 give a lot a help, by publicly certifying semi-primality. Might Paul care to try to...
... All hail the great godess Obscurity, saving the day once again! ... Well, I don't have a machine with multiple gigabytes of RAM, which would be necessary...
... Paul Leyland quite correctly remarked that Arjen's database is private. However, the GCD idea seems to work OK: ...
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Paul Leyland
paul@...
Feb 15, 2012 7:02 pm
... Two things. 1) Never ascribe to malice that which is adequately explained by incompetence. 2) I never said your algorithm couldn't work, only that it might...
