Euclid also gives a proof of the Fundamental Theorem of Arithmetic: Every integer can be written as a product of primes in an essentially unique way.Įuclid also showed that if the number 2 n − 1 2^ - 79 n + 1601 n 2 − 7 9 n + 1 6 0 1 which is prime for 0 ≤ n ≤ 79 0 ≤ n ≤ 79 0 ≤ n ≤ 7 9. PrimePages: prime number research records and result. The property of being a prime or not is called as primality List of prime numbers up to 1 000 000 000 000 (1000 billion) Prime number per page. This is one of the first proofs known which uses the method of contradiction to establish a result. 2 is the smallest even prime number of all. In Book IX of the Elements, Euclid proves that there are infinitely many prime numbers. You can see more about these numbers in the History topics article Perfect numbers.īy the time Euclid's Elements appeared in about 300 BC, several important results about primes had been proved. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has divisors 1, 2, 4, 7 and 14 and 1 + 2 + 4 + 7 + 14 = 28.Ī pair of amicable numbers is a pair like 220 and 284 such that the proper divisors of one number sum to the other and vice versa. In addition to being palindromic, it has 31 digits which is. They understood the idea of primality and were interested in perfect and amicable numbers.Ī perfect number is one whose proper divisors sum to the number itself. My personal favorite prime number is Belphegors prime: 10000000000000136660000000000000131. The mathematicians of Pythagoras's school (500 BC to 300 BC ) were interested in numbers for their mystical and numerological properties. Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians.
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