Recent content by PeterJ1

Doh! On reflection the answer to the second question is obvious. Consider it answered.

Thanks Greg. "... to factor a 232-digit number (RSA-768) utilizing hundreds of machines took two years and the researchers estimated that a 1024-bit RSA modulus would take about a thousand times as long.[1]" This helps with the second question but not the first, which is my main question.

A slightly odd layman's question about factoring large numbers and comparing two calculations. Call N a number with 1050 digits. 1) Factorise N 2) Multiply the primes sequentially from 2 onwards until the product is as close as possible to N. Would calculation 2 be significantly easier...

Bump This seems a naive question but a reasonable one and I really would like to hear a response from a mathematician. You could think of it as charity work with the mathematically impaired. :)

Hi HallsofIvy -Thanks for replying. I'm not assuming anything at all (I hope). I'm wondering whether it is possible to calculate the changing probability of N being a product of a prime as the products of each prime in turn are sieved out. This is easy for the primes 2.3 and 5. This leaves 8...

Ha. Thanks Petek. The inc-exc approach does seem relevant but I wouldn't know how it can be used in this situation. I suspect that the calculation cannot be done directly but that a result can be approximated using the PNT. But I'm not sure about this. Now I look at it I wonder if I'm just...

I am not a mathematician but enjoy studying the primes as a mechanical system. Regrettably I don't have the tools (and perhaps the intellect) for some jobs. I've spent some time trying to calculate the probability of a number being a product of each successive prime as the number line is...

Re: Problem of Calculating Probabilitiers Yep. Having 2 as a factor. Er, one in every two numbers is divisible by 2.

I hope this question is in the right place. I'm trying to calculate probabilities and struggling. Hopefully someone can help. Suppose I want to calculate the probability of N being a product of a prime below sqrt N. N will have a 1:2 chance of being a product of 2. If N is not a product...

I think a dictionary would explain these things more effectively than I could here since it would be a long answer. A quick google will do it.

As a philosopher rather than a mathematician I would add a proviso because it is a very important one that is often (perhaps usually) ignored by philosophers. A statement can be true, false, meaningless or undecidable but the LEM and LNC can only be applied legitimately to true contradictory...

Hmm. No more replies so maybe I've gone off-piste. I'll leave this one and come back with an updated and more clear question on a new thread. Thanks.

Thank you for your very clear replies, Opalg. Now you've helped me simplify the problem I was able to find a table online. Here's my attempt to do the calc. The 500th prime is 3571 The sum of the reciprocals of the primes to 3571 is 2.365328 3571 is the is the square root of 12752041...

Oh yes. I meant P to P#. Right. I think I get this now. This is the exact answer I needed so many thanks. I'll give it some more thought but I may be sorted now. Much appreciated...

As usual I replied too hastily. It was a great answer but I realized later that I didn't fully understand it. Then I realized that I may be over-complicating things. Is what follows correct? The product of the primes up to P is very soon so large compared to P that I might as well forget the...