N is the product of all the prime numbers less than 100.

Determine the last three digits of N.

*** For an extra challenge, solve this puzzle without the aid of a computer program.

Child of 5: Daddy, I must solve this problem without the aid of a computer program!
  
Father: A002110 in Sloane contains a list. It's the entry corresponding to the largest prime less than 100. 
 
Child of 5(Much later): Daddy, which number is the largest prime less than 100? 
 
Father: Never mind, try A034386 in Sloane, which has a list of the primorials n# = product of primes <= n. It's the one with "100'next to it. 
 
Child of 5(Reading): So the number is 100 2305567963945518424753102147331756070 and the last 3 digits are 070.  

Father: And you did it all without a computer program! My son, you are the new Newton.

Posted by broll on 2011-10-19 12:02:16