No
Its clear
Proofs that there are infinitely many primes. Well over 2000 years ago Euclid proved that there were infinitely many primes.Well over 2000 years ago Euclid proved that there were infinitely many primes. Since then dozens of proofs have been devised and below we present links to several of these. (Note that [Ribenboim95] gives eleven!) My favorite is Kummer\’s variation of Euclid\’s proof.
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Let there be finite number of positive prime number\xa0a1,\xa0a2,\xa0a3\xa0…….,\xa0an\xa0.\xa0Such that\xa0a1<\xa0a2<\xa0a3\xa0< .......an+\xa0<\xa0an.Let\xa0m\xa0= 1 + a1,\xa0a2,\xa0a3\xa0.......,\xa0an\xa0. It is near that\xa0a1,\xa0a2,\xa0a3\xa0.......,\xa0an\xa0is divisible by\xa0a1,\xa0a2,\xa0a3\xa0.......,\xa0an\xa0.\xa0m\xa0is a prime number or it has factors other than\xa0a1,\xa0a2,\xa0a3\xa0.......,\xa0an\xa0. There exits a positive prime number other than\xa0a1,\xa0a2,\xa0a3\xa0.......,\xa0an\xa0.This contradicts the fact that there are finite number of positive primes.Hence, there infinite number of positive primes.