偶数素数对数D(2^n)的密度系数

小草

yangchuanju 发表于 2024-3-21 23:00
A006307
Number of ways writing 2^n as unordered sums of 2 primes.

谢谢杨先生提供那么多数据，现在没有其它的方法能得到密度系数的极值，计算速度又赶不上，如果将来计算速度能够飞跃发展的话，它的极值一定能算出来。

小草

D(2^31)=2147483648*0.72886821320082046284613475785209/ln^2(2147483648)=3390038
D(2^32)=4294967296*0.72640330155687726765111827156747/ln^2(4294967296)=6341424
D(2^33)=8589934592*0.72432122125723194526556675968238/ln^2(8589934592)=11891654
D(2^34)=17179869184*0.7220968843928303175575602598626/ln^2(17179869184)=22336060
D(2^35)=34359738368*0.72001059085452391354902926448808/ln^2(34359738368)=42034097
D(2^36)=68719476736*0.71842543966184088995434564860448/ln^2(68719476736)=79287664
D(2^37)=137438953472*0.71647102329302755725738342263394/ln^2(137438953472)
=149711134
D(2^38)=274877906944*0.71497349047791861873757953048099/ln^2(274877906944)
=283277225
D(2^39)=549755813888*0.71342787379046247684046153109824/ln^2(549755813888)
= 536710100
D(2^40)=1099511627776*0.71199448484608189841773820859863/ln^2(1099511627776)
=1018369893

小草

D(2^41)=2199023255552*0.71060479875047193396056338808794/ln^2(2199023255552)
=1934814452
D(2^42)=4398046511104*0.70929533965363950461906840342869/ln^2(4398046511104)
=3680759328
D(2^43)=8796093022208*0.70806263733418537112649877804549/ln^2(8796093022208)
=7010898161
D(2^44)=17592186044416*0.70688790842110316170759953968481/ln^2(17592186044416)
=13369466800
D(2^45)=35184372088832*0.70575979705327683780692217751198/ln^2(35184372088832)
=25522944188
D(2^46)=70368744177664*0.7046917136019700861856120576072/ln^2(70368744177664)
=48776696083
D(2^47)=140737488355328*0.70367837635467770566366509942336/ln^2(140737488355328)
=93311971184
D(2^48)=281474976710656*0.70269959657816281176724687121285/ln^2(281474976710656)
=178680063951
D(2^49)=562949953421312*0.70177097075977616871975419374247/ln^2(562949953421312)
=342469661688
D(2^50)=1125899906842624*0.7008777346969917384192984841651/ln^2(1125899906842624)
=656978437719

愚工688

  G(2^41)=   G( 2199023255552 ) = 1934814452;
  G(2^42)=  G( 4398046511104 ) = 3680759328;
  G(2^43)= 7010898161,
  G(2^44)= 13369466800,
  G(2^45)= G( 35184372088832 ) = 25522944188 ,
  G(2^46)= G( 70368744177664 ) = 48776696083 ,
  G(2^47)= G( 140737488355328 )= 93311971184 ，
  G(2^48)= G( 281474976710656 )= 178680063951 ，
  G(2^49)= G( 562949953421312 )= 342469661688 ,
  G(2^50)= G(1125899906842624 )= 656978437719 ,

小草

愚工688 发表于 2024-3-29 14:55
G(2^41)=   G( 2199023255552 ) = 1934814452;
  G(2^42)=  G( 4398046511104 ) = 3680759328;
  G(2^4 ...

谢谢愚工688提供那么多数据！