Prime Number Assignation

The most essential feature of using a random number to find a potential prime number is the ordinal assignation to prime numbers. Since 2 and 3 gave us the first seven prime numbers, the spreadsheet can be expanded all the way to 23 squared, or 529. On the spreadsheet, 529 is located in the 6x+1 column when x= 88. If we assign 23 as the seventh prime, it will facilitate the test for primes. The spreadsheet indicates that before 529, only 174 numbers are necessary to look for prime numbers. All 174 numbers are located on the 6x±1 columns. Essentially, we can choose any number at random using the following equations located on the spreadsheet:

x = N (N is a natural number, will yield 2 results)

6x-1 =  P (left side potential prime) *

6x+1 = P (right side potential prime) *

*Note: when selecting P = 6x±1, ensure P is a natural odd number greater than 4. The equation must not yield a decimal result. 

The next step is to divide by the assigned primes, depending on the location of the random number. If the number is P = 89, then divide P by 5, 7, and 11. If 89 is not divisible by 5, 7, and 11 then the number is prime. This eliminates the need to check 89 by dozens of divisors. Location is everything. 89 is located between 49 and 121 or the square of prime numbers 7 and 11. The squares are the prime limits. Those limits, limit the number of divisors to check from primality. If you look at the spreadsheet, the square primes are in bold in the 6x+1 column. 5 is the first prime. The second prime 7. The third prime 11 and so on. Every time a prime number is found, then it is another prime limit by squaring it. When squaring a prime, solve for x using the equation P = 6x+1. x will yield the row its located in.