Thread: Smallest prime number

1. Smallest prime number

Find the smallest prime number N such that the following is true:The largest prime factor of N1 is A;
The largest prime factor of A1 is B;
The largest prime factor of B1 is 7.
Actually, i m not able to proceed in the problem. it seems kind of a weird question.

2. Re: Smallest prime number

Start with the fact that B is a prime number and B-1 has a prime factor of 7. So we need to test multiples of 7 and see which is the first such that adding one to it gives a prme number. For example: If B-1 = 7 then B=8, which is not prime, so we try B-1 = 2x7 = 14, which yields B=15, and that's not prime eiter. Keep going until you find a multiple of 7 that works (it won't take too long), and then B is the prime which is one more than that multiple. Once you have a value for B, apply the same technique to find A: test multiples of B until you get to one that is one less than a prime number. Finally once you have A you can find N using the same technique again.

Post back with what you get for an answer.