i***0
发帖数: 8469 | 1 World records
Current records
This table lists the current best upper bounds on Hm - the least quantity
for which it is the case that there are infinitely many intervals n, n+1,
ldots, n+H_m which contain m + 1 consecutive primes - both on the assumption
of the Elliott-Halberstam conjecture, without this assumption, and without
EH or the use of Deligne's theorems. The boldface entry - the bound on H1
without assuming Elliott-Halberstam, but assuming the use of Deligne's
theorems - is the quantity that has attracted the most attention. The
conjectured value H1 = 2 for H1 is the twin prime conjecture.
m Conjectural Assuming EH Without EH Without EH or Deligne
1 2 12 272 272
2 6 272 395,122 493,408
3 8 52,130 24,490,410 33,661,442
4 12 493,408 1,523,781,850
5 16 4,316,466 82,575,303,678
m displaystyle (1+o(1)) m log m displaystyle O( m e^{2m} ) exp((
4 - frac{52}{283} + o(1)) m) exp((4 - frac{4}{43} +o(1)) m) |
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