Classification |
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| 2, 3 and 7 are not classfied. |
| Zone 1 : primes for which k(n) <= L(n) or primes classified by weight. We have the following relation : |
| g(n) + 1 <= k(n) <= sqrt(l(n)) <= L(n) <= l(n) / 3 |
| For the first 50 000 000, 82,89 % of prime numbers are classified by weight. |
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| Zone 2 : primes for which k(n) > L(n) or primes classified by level. We have the following relations : |
| L(n) < sqrt(l(n)) < k(n) <= l(n) ; |
| L(n) + 2 <= g(n) + 1 <= k(n) <= l(n) |
| For the first 50 000 000, 17,11 % of prime numbers are classified by level. According to the numerical data, the prime numbers classified by level are rarefying (see the conjectures). |
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| Primes for which g(n) > sqrt(l(n)) are : 2, 3, 5, 7, 13, 19, 23, 31, 113 for n <= 5.10^7. |
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| Exemple : |
| n |
p(n) |
g(n) |
p(n+1) |
k(n) |
L(n) |
l(n) |
| 76 |
383 |
6 |
389 |
13 |
29 |
377 |
| 102 |
557 |
6 |
563 |
19 |
29 |
551 |
| 4334 |
41413 |
30 |
41443 |
1427 |
29 |
41383 |
| 6853 |
68963 |
30 |
68993 |
2377 |
29 |
68933 |
| 7285 |
73783 |
36 |
73819 |
2543 |
29 |
73747 |
| 9113 |
94483 |
30 |
94513 |
3257 |
29 |
94453 |
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| The two first primes (p(76) and p(102)) are in zone 1 and are classified by weight, the other primes are classified by level. |
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| arXiv:0711.0865 : Decomposition into weight * level + jump and application to a new classification of prime numbers |
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