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    regulator161's Avatar
    regulator161 Posts: 1, Reputation: 1
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    #1

    Oct 20, 2010, 09:37 AM
    What to prime numbers multiplied together equals a four hundred digit number?
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Oct 20, 2010, 09:47 AM

    See discussion here:

    https://www.askmehelpdesk.com/math-s...ber-49928.html

    I'm curious as to what course you're taking that asks this?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #3

    Oct 20, 2010, 02:02 PM

    I have seen this same question asked at least a dozen times since I began on this site. I do not know what signficance it holds that makes it so 'in demand'.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #4

    Oct 20, 2010, 02:42 PM

    Maybe we can finally put this one to bed! Because this question keeps coming up every year or so, I decided to so some research. What I found is that the 15th Merseinne prime is:



    and it is 386 digits long. It's rounded value is 1.041 x 10^385. (for reference, see: Integer Lists: Mersenne Primes)

    Multiply this by a 15 digit prime, and you'll have a 400-digit number. So how to find a 15-digit prime? Use a "prime checker," available here: Big Primes: large list of prime numbers
    and test odd numbers starting with 100000000000001 until you hit a prime. Doing this I find that 100000000000031 is prime.

    So multiply these two numbers together, and you'll have a 400-digit number that is the product of 2 primes.
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