Posted by: fortunefaded October 6, 2008
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The above statement is incorrect. Actually, it is not a prime.
Proof: (By counter-example)
2*3*5*7*11*13 + 1 = 30031 = 59 * 509
May be you are looking into the proof of infinitudes of prime. Euclid used the p1*p2*p3*....*pn +1 to prove the fact that there are infinite primes, but it does not mean that p1*p2*p3...*pn +1 has to be a prime number itself. That is the second part of the theorem.
Hope this helps.
Proof: (By counter-example)
2*3*5*7*11*13 + 1 = 30031 = 59 * 509
May be you are looking into the proof of infinitudes of prime. Euclid used the p1*p2*p3*....*pn +1 to prove the fact that there are infinite primes, but it does not mean that p1*p2*p3...*pn +1 has to be a prime number itself. That is the second part of the theorem.
Hope this helps.