How to Find Primes Anywhere in the Number Line, Fast & Efficiently, No Matter How Large 

How to Find Primes Anywhere in the Number Line, Fast &
Efficiently, No Matter How Large
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By Herb Wiggins, M.D.; Clinical Neurosciences; Discoverer/Creator of the Comparison Process/CP Theory/Model; 14 Mar. 2014.
Copyright © May 2020
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This is based upon the Wiggins Prime Sieve, which has shown that there are only 8 places in every 30 digits which can be primes. Those occur no where else.
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Because the prime quartets occur in repeating cast out 3 Remainder 0, 1 and 2 (Rem0, Rem1, Rem2) throughout the entire number line.  Those positions are invariant throughout the entire number line.
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Therefore NO matter how large the primes are, if we locate the Rem1 quartet by summing up the total of the numbers to the left of any number  of digits, then divide by three, we will only find 0, 1, 2, remainders. Because the Rem1 has 4 possible primes ending in -1, -3, -7, 9., only those can be primes . There are only 2 primes possible in the Rem0 quartet of 1, 3, 7, 9, viz, 1 and 7.  In Rem2 only the 3 and 9 ending numbers can be prime. Thus the largest number of primes is found in the Rem1 quartet, and often more in  than in the Rem2 & Rem0 combined, as well. Thus we need only test the Rem1 quartets to find  the most primes.
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As this is a compound method, we know that it works. For instance in Dugas and O’Connor, out of the Technical Uni of Tenn.:
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They found over 54 Million primes to 1 billions And listed the last 50 known primes up to 1 Billion. IN EVERY case each of those primes fell in the exact sites  allowable in the Rem1, 2, & 3 quartets. And that proves that the method works even to 1 billions.
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Thus we can locate primes very easily using this compound method. The Wiggins Prime Sieve shows easily by the c/o 3 remainder method where the Rem1, & all primes possible sites are targetable anywhere, no matter how high.
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Thus by using a prime certification method on ONLY those 4 sites in any number of any digits long, we can ID primes without limit as long as the computer can sum up the totals of the digits and cast out 3, thus locating the Rem1 quartets anywhere. IN addition, for no matter how high the primes are, we can always find larger primes, without limits. This is done by simply adding 30 to the largest known prime, and then locating the next Rem1 quartet higher and lower than that. Easily, repeatedly, & efficiently.
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Effectively 4 of every 30 numbers has the Rem1 primes sites, Thus out of 30 numbers only 2/15 of the number line need be only looked at. That greatly simplifies the search. And in addition using the prime squared +2, then +4, then plus 2, and then +4, etc., we generate primes composites very simply, and quickly, and reduce down the number line easily by 92% more, Giving, eventually only by taking out primes from 7 to 23. IF using primes up to 61, nearly 99+% of the number line can be removed. And thus speed up the finding of the primes by the well known AKS prime identifier process, which is the fastest known.
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Thus by this method, for no matter how high the primes of whatever length of digits, we can locate higher primes at will and with a simple method., Thus speeding up the ID’g of primes by 100’s, & even 1000’s of times faster then current methods.
This also weighs in on the twin prime question quite easily and simply.  Because there are ONLY 3 places in the 1, 3, 7, 9 quartets of Rem1, 2, & 3, where there are twin primes, Twice in Rem 1, viz -1 & -3, and -7 and -9. The other is from the transition from Rem2 -9 to Rem0 -1. From 19 to 21 the 21 is not prime. From 29 to 31 is IS prime. that is from Rem 2 to Rem0. From 39 to 41, that is from Rem0 to Rem1, again, 39 site is always not a prime. Thus, ONLY in those 3 sites can there be twin primes. That vastly reduces the searches for confirmation of the Twin Prime Hyp.
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IN working through the number line up to 1 billion, we find exactly those same conditions. Thus it can be proven by exhaustion and simple logic, that twin primes can be found anywhere in the number line, tho they become less common as the number of digits increases. Still, it’s highly likely that twin primes exist without limits, and thus can be easily proven by the Wiggins Prim Sieve quartets method, as well.
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This largely states the proofs that the twin prime hypothesis is the case. & once the formal logical proof can be sorted thru and created, very, very simply proves the Twin Prime hypothesis, as well.
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Thus the Magic of the Wiggins Prime  Sieve.
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& also shows that Goldbach’s is both true, not true, and at very high numbers where the primes because so very rare, is possibly not true, as well.