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

By David Wells

A interesting trip into the mind-bending international of leading numbers
Cicadas of the genus Magicicada look as soon as each 7, thirteen, or 17 years. Is it only a accident that those are all leading numbers? How do dual primes range from cousin primes, and what in the world (or within the brain of a mathematician) will be horny approximately major numbers? What did Albert Wilansky locate so attention-grabbing approximately his brother-in-law's telephone number?
Mathematicians were asking questions on leading numbers for greater than twenty-five centuries, and each solution turns out to generate a brand new rash of questions. In best Numbers: the main Mysterious Figures in Math, you are going to meet the world's such a lot proficient mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you may find a host of certain insights and artistic conjectures that experience either enlarged our realizing and deepened the mystique of best numbers. This complete, A-to-Z consultant covers every little thing you ever desired to know--and even more that you simply 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 good net Mersenne leading Search
* and lots more and plenty, a lot more

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Which are the primorials, the result of multiplying the consecutive primes together. Is this true? Marek Wolf, Odlyzko, and Rubinstein say yes. (Rivera, Conjecture 10) Chinese remainder theorem Sun Tsu Suan-ching (fourth century AD) posed this problem: “There are certain things whose number is unknown. Divided by 3, the remainder is 2; by 5 the remainder is 3; and by 7 the remainder is 2. ” The solution is 23. (Wells 1992, 23) This is an example of the Chinese remainder theorem, which says that if you know the remainders when N is divided by n numbers, which are coprime in pairs, then you can find a unique smallest value of N, and an infinity of other solutions, by adding any integral multiple of the product of the n numbers (or subtracting if you are satisfied with negative solutions).

G. L. Honaker Jr. found this one: 373, 131713, 111311171113, 311331173113. Unfortunately, the next term is composite. Carlos Rivera, Mike Keith, and Walter Schneider have subsequently found six-term sequences, and Schneider has found a seven-term sequence starting with 19,972,667,609. (Schneider 2003) (Rivera, Puzzle 36) Dickson’s conjecture Leonard Eugene Dickson (1874–1954) is best known today for his extraordinarily detailed three-volume History of the Theory of Numbers, whose first volume is on Divisibility and Primality.

Catalan’s Mersenne conjecture When Lucas proved in 1876 that 2127 − 1 is prime, Catalan noticed that 127 = 27 − 1 and conjectured that this sequence, where Mp is the pth Mersenne number, contains only primes: = M2 C1 = 22 − 1 = 3 C2 = 2C1 − 1 = 23 − 1 = M3 = 7 C3 = 2C2 − 1 = 27 − 1 = M7 = 127 C4 = 2C3 − 1 = 2127 − 1 = M127 = 170141183460469231731687303715884105727 and so on . . Unfortunately, C5 has more than 1038 digits and so cannot be tested directly, though Curt Noll has verified that C5 has no prime divisor less than 5 и 1050.

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