I already know that 3 digits times 3 digits doesn't = 6 digits
So a 20 digit number times a 20 digit number won't give me a 400 digit number..
I know it's something like 386 digit prime times 15 digit prime, but Im not sure, some help would be nice, thank you.
2006-08-16 06:15:39 · 6 answers · asked by Matthew B 2 in Science & Mathematics ➔ Mathematics
Actually a 20 digit number times a 20 digit number will give you a 40 digit number so in your case you could multiply a 200 digit number by a 200 digit number or any two number where the number of digits adds to 400.
I don't have a program that will tell me 200 digit prime numbers.
2006-08-16 06:35:58 · answer #1 · answered by rscanner 6 · 1⤊ 1⤋
Okay, so a number x has n digits exactly when
10^(n-1) <= x < 10^n.
I went to a list of Mersenne primes and found that 2^1279-1 is prime and has 386 digits. Call it A. Moreover its first digit is 1, so
10^386
Then I used the "isprime" command of Maple several times, and eventually found that B=10^13+37 is prime. Note that
10^13
Combining these inequalities, using the fact that 386+13=399, we obtain
10^399
Therefore A*B has exactly 400 digits, thus A and B give a solution to your problem.
2006-08-16 16:34:09 · answer #2 · answered by Steven S 3 · 0⤊ 0⤋
In general an n digit number times an m digit number will yield a number with between n+m-1 digits and n+m digits (I'll leave the details of that for you to figure out. Remember all numbers are polynomials of the form
an(10)^n + a(n-1)10^(n-1).....a1*10+a0)
so your first assertation is false. Example:
999*999 = 998,001 which has 6 digits. Also
100*100 = 10,000 which has 5 digits.
The answer is that there are *lots* of 200 digit (or 200 and 201 digit numbers) which are prime. That's the thing that makes codes based on factoring so difficult to break.
Doug
2006-08-16 13:43:10 · answer #3 · answered by doug_donaghue 7 · 0⤊ 0⤋
i suggest try finding a 399 digit number and multiply it by 2 or 3. as long as the 399 digit number is greater than the 399 digit number consisting of all 3's, this will work. but of course, you have to know a 399 digit prime number first.
2006-08-16 13:30:59 · answer #4 · answered by Jon S 2 · 0⤊ 0⤋
1* any 400 diget prime number
2006-08-16 13:22:17 · answer #5 · answered by Bacchus 5 · 0⤊ 0⤋
The answer is next to impossible to find out. That is why encryption works.
2006-08-16 13:28:01 · answer #6 · answered by Barkley Hound 7 · 0⤊ 0⤋