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Show that there are infinitely many positive primes. |
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Answer» Thanks...☺☺ 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. |
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