Thursday, January 14, 2010

Infinite primes

#Problem 10
Prove that infinitely many prime numbers are possible.

Solution Scheme and approach

Let if possible there are a1, number of finite primes.
Consider another number
Now we can say,
N is such a number which can be divide by all primes but always gives a remainder 1. Hence, contradiction.
Because any number>1 should be divisible by at least one prime number.

=>Infinite primes are possible. Q.E.D.

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