There is a mathematical reason why 1 is not a prime.
http://en.wikipedia.org/wiki/Prime_number
"Primality of one
One of the primary reasons to exclude 1 from the set of prime numbers is the fundamental theorem of arithmetic, which says that every positive integer x can be uniquely written as a product of primes. When x is itself prime, this factorization has only one prime (x itself) in it, and when x = 1 the factorization is the empty product. But if 1 were admitted as a prime, then any integer could be factored in an infinite number of ways. For example, in this case the number 3 could be factored as 1k · 3 = 3 for any integer k.
More generally, in unique factorization domains, every non-zero element is a unique product of prime elements and a unit. The factorization would not be unique if products of units were allowed.
Until the 19th century, most mathematicians considered the number 1 a prime, the definition being just that a prime is divisible only by 1 and itself but not requiring a specific number of distinct divisors. There is still a large body of mathematical work that is valid despite labeling 1 a prime, such as the work of Stern and Zeisel. Derrick Norman Lehmer's list of primes up to 10,006,721, reprinted as late as 1956,[4] started with 1 as its first prime.[5] Henri Lebesgue is said to be the last professional mathematician to call 1 prime.[6] The change in label occurred so that the fundamental theorem of arithmetic, as stated, is valid, i.e., “each number has a unique factorization into primes.”[7][8] Furthermore, the prime numbers have several properties that the number 1 lacks, such as the relationship of the number to its corresponding value of Euler's totient function or the sum of divisors function.[9]"
If you have a systematic way to find prime, you will be the next Nobel prize winner. It is used in encyption coding. You will have essentially "break" all the coding and have access to ALL bank account of the world. |
2010/9/16 21:05
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2010/10/2 17:10
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