| Article |
|---|
| Article name |
PROOF OF BROKAR\'S HYPOTHESES (ON FOUR BASIC NUMBERS) |
| Authors |
Scherbakov A.. , |
| Bibliographic description |
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| Category |
Natural Sciences |
| DOI |
511 |
| DOI |
10.21209/2074-9155-2018-12-2-109-116 |
| Article type |
scientific |
| Annotation |
A natural series of numbers is presented, represented as a periodic structure consisting of alternating the first prime numbers ≤ PX (1 is the smallest simple factor> 1 of every number), where the Sieve of Eratosthenes formats these interlaces ≤ PX in the form of periodic primeval fractals located from 1 to PX # and repeated without changes with a period = PX#.
By grouping φ (PX#) of residues mod (PX#) of each successive fractal = PX# strictly by 4 consecutive residues mod (PX#) deductions and analyzing the resulting structure, the author proves Brokar’s hypothesis that the natural series of numbers contains at least four prime numbers between the squares of two consecutive primes from РХ2 to РХ + 12, and also from (РХ+ 1─2)2 to РХ + 12
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| Key words |
Key words: residue pairs; prime numbers; primordial;
sieve of Eratosthenes; alternations; fractal
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| Article information |
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| References |
References
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| Full article | PROOF OF BROKAR\'S HYPOTHESES (ON FOUR BASIC NUMBERS) |
