400-Digit Product of Two Primes
Date: 11/04/2002 at 15:24:38 From: Scott Slovak Subject: Prime numbers Hello, My question is: What two prime numbers when multiplied together will equal a 400-digit number? I've tried researching, and I don't even know where to begin. Thank you very much, Scott
Date: 11/05/2002 at 15:20:32 From: Doctor Wilkinson Subject: Re: Prime numbers Hi, Scott. I can tell you how to find this. First of all, you want to go to the Dr. Math FAQ page, http://mathforum.org/dr.math/faq/ and click on "Prime Numbers." Then click on "Mersenne Primes: History, Theorems and Lists," and you will find a list of primes of the form 2^ - 1 giving the number of digits. You should see one with 386 digits. Now if you multiply this by a number with 15 digits whose first two digits are 10, you will get a number with 400 digits, because the first digit of the big prime can easily be estimated to be no greater than 6. To find the 15-digit prime, you can start with 100000000000001 and proceed to test the odd numbers one at a time until you find a prime. To do the testing, go back to the "Prime Numbers" page and click on "The Prime Pages"; then click on "Check a Number's Primality". Good luck! - Doctor Wilkinson, The Math Forum http://mathforum.org/dr.math/
Date: 11/19/2005 at 22:58:06 From: Carmen Subject: Prime Numbers Mega Multiplication What is the product of (2^1279 - 1) * 100000000000031 = ?? I couldn't find the equipment to do the multiplication. I found what I had to do from your prime page, as well as finding the 15 digit prime, but I can't find a calculator that can accomodate these huge numbers.
Date: 11/20/2005 at 09:51:12 From: Doctor Vogler Subject: Re: Prime Numbers Mega Multiplication Hi Carmen, Thanks for writing to Dr Math. I recommend the program GNU Pari, which you can download from http://pari.math.u-bordeaux.fr/ By the way, if you are trying to make a 400-digit product of two primes, you can also pick any two numbers x and y whose product is 400 digits (such as two 200-digit numbers) and ask Pari for nextprime(x)*nextprime(y). For example, you could take x = random(10^200) y = random(10^200) nextprime(x)*nextprime(y) If you have any questions about this or need more help, please write back and show me what you have been able to do, and I will try to offer further suggestions. - Doctor Vogler, The Math Forum http://mathforum.org/dr.math/
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