By: George Lee

George Lee — Wed, 12 Dec 2018 14:43:00 +0000

In reply to Daniel Stanev. 27 and 57 are not prime.

By: William P. G. Shaw

William P. G. Shaw — Sun, 18 Feb 2018 16:38:28 +0000

Prime numbers and composite numbers can be studied using linear algebra. The fallacy is to pl;ace prime two and the infinite set of the other prime numbers into one class. Rather place [2] and [3, 5, 7, 11, … ] into these two separate classes. Every prime [not two] or composite can be represented as a unique column vector except that the number of elements in the vector has to be at least [N + 1] and can be any finite number of elements more than [N + 1]. Here the prime or composite lies in an interval between 2^{N} and 2^{N + 1}, where N = 1, 2, … For example, 23 lies between 2^{4} and 2^{5}.
23 = 2^{4} + 2^{3} + r[1].2^{2} + r[2].2^{1} + r[3].2^{0} The remainders are seen to be r[1] = – 1,
r[2] = 1 and r[3] = 1. As a vector, 23 is: [16, 8, – 4, 2, 1]. The remainders are found by dividing an uneven integer sucessively by two to give an uneven quotient and the remainder that may be either + 1 or – 1. repeating this process for a succession of primes or composites gives column vectors to fill up a matrix of coefficients, resulting in a system of linear homogeneous equations. The non-zero exponents of prime two cancel in the linear equations leaving only the reminders: [1, 1, – 1, 1, 1], in the case of prime 23. The number of components in a vector representing an uneven number can be increased in view of the fact that: 2^{N} = 2^{N + 1} – 2^{N} and likewise: 2^{N + 1} = 2^{N + 2} – 2^{N + 1] etc.
It just looks very much like linear algebra is the key to solving the mystery of the erratic prime sequence. The sequence of the primes has remained unsolved since at least since the time of Euclid of Alexandria. Not to be confused with Euclid of Megara.

By: Kelly

Kelly — Wed, 04 Jan 2017 14:07:11 +0000

In reply to Boris Sklyar. True but NOT lololololololololololol

By: Kelly

Kelly — Wed, 04 Jan 2017 14:05:38 +0000

In reply to Saurabh Sonparote. So true so true lolololololololollololololololololololololololololololololololololololololololololololololllolololololololololololololololololololololololololololololololololololololololololololololololololololololllololololololololOlolololololololololololllololololololololololololololololOloloollolololololololOlololol

Comments on: Another Look at Prime Numbers

By: George Lee

By: William P. G. Shaw

By: Kelly

By: Kelly