values of $4^n$ and ${\displaystyle \prod \mathrm{@}\mathrm{@}\mathrm{@}{\mathrm{@}}_{i=1}^{\pi (n)}{p}_i}$ for

The following table is in of the statement that

$$4^x>\prod _{i=1}^{\pi (x)}{p}_i$$

is always true for any nonnegative $x$.

$n$	$4^n$	${\displaystyle \prod _{i=1}^{\pi (n)}}{p}_i$	$4^n-{\displaystyle \prod _{i=1}^{\pi (n)}}{p}_i$
1	4	1	3
2	16	2	14
3	64	6	58
4	256	6	250
5	1024	30	994
6	4096	30	4066
7	16384	210	16174
8	65536	210	65326
9	262144	210	261934
10	1048576	210	1048366
11	4194304	2310	4191994
12	16777216	2310	16774906
13	67108864	30030	67078834
14	268435456	30030	268405426
15	1073741824	30030	1073711794
16	4294967296	30030	4294937266
17	17179869184	510510	17179358674
18	68719476736	510510	68718966226
19	274877906944	9699690	274868207254
20	1099511627776	9699690	1099501928086
21	4398046511104	9699690	4398036811414
22	17592186044416	9699690	17592176344726
23	70368744177664	223092870	70368521084794
24	281474976710656	223092870	281474753617786
25	1125899906842624	223092870	1125899683749754

Title	values of $4^n$ and ${\displaystyle \prod \mathrm{@}\mathrm{@}\mathrm{@}{\mathrm{@}}_{i=1}^{\pi (n)}{p}_i}$ for
Canonical name	ValuesOf4nAnddisplaystyleprodi1pinPiFor0N26
Date of creation	2013-03-22 17:04:51
Last modified on	2013-03-22 17:04:51
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	5
Author	PrimeFan (13766)
Entry type	Example
Classification	msc 11N05
Classification	msc 11A25
Classification	msc 11A41