10^18 と Cino's prime3での10^25で、fitValを求める

2008/05/04）16:55
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素数生成式でのfitValを求めてみる。
再掲）変数：fitValを含む式は以下となる。
so = Math.sin(x) + x/2.0d * Math.log(x) + x * Math.pow(Math.log(x), (1.0d - 2.0d/(Math.PI * Math.log(x)) - fitVal));
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Actual data.
n, (10^n)-th prime
1,29
2,541
3,7919
4,104729
5,1299709
6,15485863
7,179424673
8,2038074743
9,22801763489
10,252097800623
11,2760727302517
12,29996224275833
13,323780508946331
14,3475385758524527
15,37124508045065437
16,394906913903735329
17,4185296581467695669
18,44211790234832169331

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n,fitVal,diff
1, 0.016697270863700153, 7.105427357601002E-15
2, 0.11828509884629772, 1.1368683772161603E-13
3, 0.13371339451737424, 9.094947017729282E-13
4, 0.1339372838724045, 1.4551915228366852E-11
5, 0.13450059066571043, 4.6566128730773926E-10
6, 0.1354188950308203, 3.725290298461914E-9
7, 0.13643593814870322, 5.9604644775390625E-8
8, 0.13712705473049472, 2.384185791015625E-7
9, 0.13763566320049875, 7.62939453125E-6
10, 0.13796070887153472, 3.0517578125E-5
11, 0.13813672367866428, 4.8828125E-4
12, 0.13819192752694057, 0.00390625
13, 0.13815218496828055, 0.0625
14, 0.13803809069118347, 1.0
15, 0.1378660578548974, 8.0
16, 0.1376490335884353, 64.0
17, 0.13739721815320907, 512.0
18, 0.1371186515643004, 8192.0
diff_max=8192.0
diff_min=7.105427357601002E-15
diff_avg=487.6148296100252
level=20
patNo=0(with sin)

～～～
Cino's prime3では、、、
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Calculated data
n prime3(10^n)
1,29
2,536
3,7923
4,104768
5,1299733
6,15484040
7,179431239
8,2038076587
9,22801797576
10,252097715777
11,2760727752353
12,29996225393465
13,323780512411510
14,3475385760290723
15,37124508056355511
16,394906913798224975
17,4185296581676470068
18,44211790234127235470
19,465675465111725379481
20,4892055594601460009775
21,51271091498034649094620
22,536193870744433106620493
23,5596564467987648427919029
24,58310039994835091909014516
25,606527267811196246600510442

***
n,fitVal,diff
1, 0.016697270863700153, 7.105427357601002E-15
2, 0.1288894823072039, 1.1368683772161603E-13
3, 0.13324998970352347, 9.094947017729282E-13
4, 0.13363803601607202, 1.4551915228366852E-11
5, 0.13448702563443884, 2.3283064365386963E-10
6, 0.13549983834834448, 3.725290298461914E-9
7, 0.1364120411478801, 5.9604644775390625E-8
8, 0.13712648812547937, 4.76837158203125E-7
9, 0.13763475925866678, 3.814697265625E-6
10, 0.13796090636334704, 3.0517578125E-5
11, 0.13813663053504516, 4.8828125E-4
12, 0.1381919067155137, 0.00390625
13, 0.13815217911301042, 0.125
14, 0.13803809041830092, 0.5
15, 0.13786605769436383, 8.0
16, 0.13764903372728024, 64.0
17, 0.13739721812765832, 1024.0
18, 0.13711865157235853, 8192.0
19, 0.13681968947826093, 65536.0
20, 0.1365053716004467, 2097152.0
21, 0.1361797078753624, 8388608.0
22, 0.13584589897768176, 1.34217728E8
23, 0.13550650672215972, 1.073741824E9
24, 0.13516358615133844, 8.589934592E9
25, 0.13481878837582156, 1.37438953472E11
diff_max=1.37438953472E11
diff_min=7.105427357601002E-15
diff_avg=5.889896328025177E9
level=20
patNo=0(with sin)
～～～
fitValは、0.138 近辺で安定せず、下がり始めた、、、
FitVal did not stabilize by about 0.138, and began to fall.