T4(x)的密度系数

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T4(x)的密度系数

表T4(x)为p1+2=p2,p2+4=p3,p3+6=p4,p4+8=p5的素数组的组数.

1(347,349,353)359)367)
【】【】【】
2(1427,1429,1433,1439,1447)
3(2687,2689,2693,2699,2707)
4(4931,4933,4937,4943,4951)
【】【】【】
5(13901,13903,13907,13913,13921)
6(21557,21559,21563,21569,21577)
7(23741,23743,23747,23753,23761)
8(27941,27943,27947,27953,27961)
9(28277,28279,28283,28289,28297)
10(31247,31249,31253,31259,31267)
11(32057,32059,32063,32069,32077)
12(33617,33619,33623,33629,33637)
13(45821,45823,45827,45833,45841)
14(55661,55663,55667,55673,55681)
15(55817,55819,55823,55829,55837)
16(68207,68209,68213,68219,68227)
17(68897,68899,68903,68909,68917)
18(91571,91573,91577,91583,91591)
【】【】【】

T4(x)的密度系数

表T(x)为孪生素数对数，T3(x)为p1+2=p2,p2+4=p3,p3+6=p4,p4+8=p5的素数组的组数.

π(x)=C1*x/lnx,T(x)=C2*π(x)/lnx,T2(x)=C3*T(x)/lnx,T3(x)=C4*T2(x)/lnx,
C4*T3(x)/lnx.
T4(x)=C1*C2*C3*C4*x/ln^4(x).

π(10^3)=1.160502886868999024745067693161*10^3/ln10^3=168
T(10^3)=1.4391156831212785525112446591777*168/ln10^3=35
T2(10^3)=2.9604665481352015937374175845942*35/ln10^3=15
T3(10^3)=1.3815510557964274104107948728106*15/ln10^3=3
T4(10^3)=2.3025850929940456840179914546844*3/ln10^3=1
T4(10^3)=15.728406215343153921423005764509*10^3/ln^5(10^3)=1

π(10^4)=1.1319508317158728582632445991228*10^4/ln10^4=1229
T(10^4)=1.5363057577340255987752261943378*1229/ln10^4=205
T2(10^4)=2.471066929066780734068088390393*205/ln10^4=55
T3(10^4)=3.0142932126467507136235524497686*55/ln10^4=18
T4(10^4)=2.0467423048835961635715479597195*18/ln10^4=4
T4(10^4)=26.511749735821217474135239346266*10^4/ln^5(10^4)=4

π(10^5)=1.1043198105999443100550287016666*10^5/ln10^5=9592
T(10^5)=1.4691222653381525840481763659996*9592/ln10^5=1224
T2(10^5)=2.4361500779634715366040023969088*1224/ln10^5=259
T3(10^5)=2.8448927789887823123002211023127*259/ln10^5=64
T4(10^5)=3.2380102870228767431503004831499*64/ln10^5=18
T4(10^5)=36.408347720701745188479180010435*10^5/ln^5(10^5)=18