Number Theory

Prime numbers : the most mysterious figures in math by David Wells

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By David Wells

A interesting trip into the mind-bending global of major numbers
Cicadas of the genus Magicicada seem as soon as each 7, thirteen, or 17 years. Is it only a accident that those are all leading numbers? How do dual primes vary from cousin primes, and what on the earth (or within the brain of a mathematician) can be horny approximately top numbers? What did Albert Wilansky locate so interesting approximately his brother-in-law's cellphone number?
Mathematicians were asking questions on best numbers for greater than twenty-five centuries, and each solution turns out to generate a brand new rash of questions. In leading Numbers: the main Mysterious Figures in Math, you will meet the world's such a lot talented mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you can find a host of specific insights and creative conjectures that experience either enlarged our knowing and deepened the mystique of leading numbers. This finished, A-to-Z consultant covers every thing you ever desired to know--and even more that you just by no means suspected--about major numbers, including:
* The unproven Riemann speculation and the ability of the zeta function
* The ""Primes is in P"" algorithm
* The sieve of Eratosthenes of Cyrene
* Fermat and Fibonacci numbers
* the nice web Mersenne major Search
* and masses, a lot more

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Qxd 3/22/05 12:05 PM Page 31 conjectures • 31 is likely to be true, although they cannot prove it. Such deep conjectures have contributed enormously to the progress of mathematics. Fermat’s Last Theorem, labeled a “theorem” only because Fermat claimed to have proved it, was for centuries a plausible conjecture until it was finally proved by Andrew Wiles. Today’s most famous and hardest mathematical problem is by common consent the Riemann hypothesis, a conjecture about the distribution of the prime numbers.

Fermat’s Last Theorem, labeled a “theorem” only because Fermat claimed to have proved it, was for centuries a plausible conjecture until it was finally proved by Andrew Wiles. Today’s most famous and hardest mathematical problem is by common consent the Riemann hypothesis, a conjecture about the distribution of the prime numbers. Conjectures about prime numbers have another feature that can be both intriguing and infuriating. Because the primes are quite frequent among the “small” integers, there are many tempting conjectures that fail as soon as we get out a modern electronic calculator or a powerful computer.

Conway and Guy 1996, 107–10) • G. J. Fee and S. Plouffe have computed B200,000, which has about 800,000 digits. Bertrand’s postulate Joseph Bertrand (1822–1900) was a precocious student who published his first paper, on electricity, at the age of seventeen, but then became more notable as a teacher than as an original mathematician. Bertrand’s postulate states that if n is an integer greater than 3, then there is at least one prime between n and 2n − 2. (This is the precise theorem. ) Strangely, although it continues to be called a postulate, it is actually a theorem: it was proved by Tchebycheff in 1850 after Bertrand in 1845 had verified it for n less than 3,000,000.

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