This document discloses concepts I have discovered through my own research into the area of prime numbers. I have not borrowed any of these concepts from any other source (except where noted). They represent ideas that I have discovered over the last 18 years. Unless you are mathematically inclined it may be easier to skip the following list of highlights and go directly to the presentation that follows which makes clear the following points.
- Prime factorial (PF) numbers are the basis of computing prime numbers.
- All references to relatively prime numbers in this text are in relation to PF numbers.
- Every number relatively prime to a PF is the sum of a relatively prime number and a multiple of a PF.
- Prime numbers are a subset of numbers relatively prime to a PF.
- Relatively prime numbers occur in distinct groups or blocks called matrices.
- Every matrix is bounded on the low side by a lower PF and on the high side by the next higher PF (upper PF).
- Every prime and relatively prime number acts as a seed number for other prime and relatively prime numbers.
- All of the numbers relatively prime to the lower PF are called seed numbers of a matrix.
- Every number in a matrix is the sum of one of the seed numbers plus a multiple of the lower PF.
- Every relatively prime number X is paired to number Y in the matrix such that X plus Y equals the upper PF.
- Every matrix has a Key Seed number which is the smallest prime number in the seed list.
- Once a prime number has been used as a Key Seed in a matrix, it and all numbers in the matrix of which it is a factor, are dropped from the list of numbers that populate the seeds for the next larger matrix and will never appear again.
- The number of columns in a matrix is one less than the Key Seed number.
- The number of rows in a matrix is equal to the number of members of the next smaller matrix.
- The count of the number of numbers relatively prime to the upper PF can be computed exactly with a recursive formula using the information contained in points 13 and 14.
Note: A prime factorial is a number that is the result of a consecutive multiplication of prime numbers:
1*2=2, 2*3=6, 6*5=30, 30*7=210 etc.