primes

I want to know what the output e is 65537 (0x10001) means. It happens during the RSA Key Generation using openssl genrsa . I know that the dots mean that the number has passed a probe division and the plus is printed out after it passed a miller rabin test. But i can't figure out what the last info message before the RSA key is printed out means. I can't find it in the openssl docs. And I could use it in term paper on prime number generation. Thanks for your help! :) Raymond Tau The "e" is the public exponent, in openssl genrsa , you can use the option -F4 or -3 to choose between 65537 and 3.

Is there any nice algorithm to find the nearest prime number to a given real number? I only need to search within the first 100 primes or so. At present, I've a bunch of prime numbers stored in an array and I'm checking the difference one number at a time (O(n)?). Rather than a sorted list of primes, given the relatively small range targetted, have an array indexed by all the odd numbers in the range (you know there are no even primes except the special case of 2) and containing the closest prime. Finding the solution becomes O(1) time-wise. I think the 100th prime is circa 541. an array of

I'm truly a beginner at python so I apologise for the lack of knowledge, but the reason I'm asking is that reading the Python manual and tutorial ( http://docs.python.org/2.7/tutorial ) I'm not unable to totally grasp how loops work. I've written some simple programs so I think I get the basics but for whatever reason this program that is meant to list all primes less than or equal to n is not working: n = int(raw_input("What number should I go up to? ")) p = 2 while p <= n: for i in range(2, p): if p%i == 0: p=p+1 print "%s" % p, p=p+1 print "Done" The output when I enter 100 for example is:

How to find number of pairs of consecutive prime numbers having difference of 6 like (23,29) from 1 to 2 billion (using any programming language and without using any external libraries) with considering time complexity? Tried sieve of eratosthenes but getting consecutive primes is challenge Used generators but time complexity is very high The code is: def gen_numbers(n): for ele in range(1,n+1): for i in range(2,ele//2): if ele%i==0: break else: yield ele prev=0 count=0 for i in gen_numbers(2000000000): if i-prev==6: count+=1 prev = i Interesting question! I have recently been working on

Possible Duplicate: Help with algorithm problem from SPOJ Came across this interview question. Given two n-digit prime numbers, convert the first prime number to the second changing one digit at a time. The intermediate numbers also need to be prime. This needs to be done in the minimum number of steps (checking for primality and changing a digit are considered steps) E.g. convert 1033 to 8179 (1033->1733->3733->.......->8179) Nice challenge for a rainy Monday evening (it is here, anyway!). This can be done using Dijkstra's algorithm . The first step is to create a graph containing all 4-digit