Fundamental theorem of arithmetic

[AntonioLao]

It was Euclid in 300 B.C. who first attempted a theory of numbers, the study of the properties of whole numbers and ratios of whole numbers. This theory can only be found in Books VII, VIII, and IX of his Elements. In them Euclid represents numbers as line segments and the product of two numbers as rectangle. These geometric representations were supported by verbal arguments and proofs in contrast to modern usage of symbols. He did prove the non-existence of a largest prime number by reduction ad absurdum that is based on the false assumption that there is a largest prime.

To this day, the theory of prime numbers remains unsolved even though many conjectures exist. The one listed in the Millennium Problems is known as the Riemann Hypothesis with a prize tag of $1 Million for the person or persons proving it correctly. Analogous to Goldbach conjecture that every even whole number greater than 2 is the sum of two primes and even though it is not proved or disproved, the fundamental theorem of arithmetic was proved by basic axioms on whole numbers as from a unique factorization theorem of prime decomposition. Simply stated, it says that every composite number can be decomposed into at least two prime factors. For examples: 4=2x2, 9=3x3, 8=2x2x2, 15=3x5, and 12709189=3559x3571. In the science and technology of modern encryption the larger the prime factors are the more secure the coded signals become. In 1903, Frank Nelson Cole (1861-1926) showed that 2 raised to 67th power minus 1 is a composite number with two prime factors: 193707721 and 16183257287.

[austintorn@aol.com]

Remember the guy who spent years on figuring pi to thousands of digits by using only a pencil, but then had to start all over because he make a mistake in position 712?

Also, it is said that a quantum computer could unencrypt large primes and find the factors instantly.

Also, I think numbers started out as having n number of line segments in each.

[AntonioLao]

what we need to find out is what algorithm these claims are using.

[mkirkpatrick]

When you add it all up my friend,what does it REALLY amount to!




regards michael.

[AntonioLao]

nothing short of infinity. By the way, the uses of prime factors are in enscription such as the security of all internet access.

[mkirkpatrick]

nothing short of infinity. By the way, the uses of prime factors are in enscription such as the security of all internet access.

Anything shorter would not cut the mustard!




regards michael.

[AntonioLao]

Or the custard.

[mkirkpatrick]

Or the custard.

Fancy me for omitting the custard,I;ll forget the rhubarb next!





regards michael.

[AntonioLao]

To exercise your memory is one way to memorize the first billion prime numbers.

[mkirkpatrick]

To exercise your memory is one way to memorize the first billion prime numbers.

I will start on that first thing tomorrow.




regards michael