Relationships between Prime-Rich Euler Type Equations and a Triangular Array of the Odd Integers,
Abstract
A certain triangular array of the odd integers, which is built up along successive diagonals of a rectangular grid, is correlated with equations of the form x squared-x+c, c=2n-1, n+1,2,3... where n indicates the number of the column (and also the row number for equations x squared + x - r). 'Primitive' cell arrays are derived from the above array. Each such array consists of a prime value p(of c) which is substituted for every integer in the triangular array who is identical to 0(mod p) with all other locations corresponding to integers not identical to (mod p) left blank. Various relationships between the triangular array, the equations x squared - x + c, c=1,3,5,... and the derived primitive cell arrays are brought out. These show how (1) Euler type prime-rich equations can be found; (2) Why and how non-random structure exists in the way prime numbers occur in the sequence of the positive integers 1,2,3.... Originator-supplied keywords: Prime numbers, Non-random structure, Euler Type equations, Prime-Rich equations, Sieve for primes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1985
- Accession Number
- ADA157928
Entities
People
- R. S. Sery
Organizations
- Naval Ordnance Laboratory