Self similarity...............fractals.........patterns........there are exactly 4 primes in the 1st 10 numbers..........................which is exactly the same percentage as in the 1st 100 numbers..............1/4 or 25%.....................................................100/25 = 4.............................

Table of π(x), x/log x, and li(x)[edit]

The table compares exact values of π(x) to the two approximations x/log x and li(x). The last column, x/π(x), is the average prime gap below x.

x	π(x)	π(x) − x/log x	π(x)/x / log x	li(x) − π(x)	x/π(x)
10	4	−0.3	0.921	2.2	2.500
102	25	3.3	1.151	5.1	4.000
103	168	23.0	1.161	10.0	5.952
104	7003122900000000000♠1229	143.0	1.132	17.0	8.137
105	7003959200000000000♠9592	906.0	1.104	38.0	10.425
106	7004784980000000000♠78498	7003611600000000000♠6116.0	1.084	130.0	12.740
107	7005664579000000000♠664579	7004441580000000000♠44158.0	1.071	339.0	15.047
108	7006576145500000000♠5761455	7005332774000000000♠332774.0	1.061	754.0	17.357
109	7007508475340000000♠50847534	7006259259200000000♠2592592.0	1.054	7003170100000000000♠1701.0	19.667
1010	7008455052511000000♠455052511	7007207580290000000♠20758029.0	1.048	7003310400000000000♠3104.0	21.975
1011	7009411805481300000♠4118054813	7008169923159000000♠169923159.0	1.043	7004115880000000000♠11588.0	24.283
1012	7010376079120180000♠37607912018	7009141670519300000♠1416705193.0	1.039	7004382630000000000♠3