# values of $4^{n}$ and $\displaystyle\prod@\slimits@@@_{i=1}^{\pi(n)}p_{i}$ for $0

The following table is in of the statement that

 $4^{x}>\prod_{i=1}^{\pi(x)}p_{i}$

is always true for any nonnegative $x$.

 $n$ $4^{n}$ $\displaystyle\prod_{i=1}^{\pi(n)}p_{i}$ $\displaystyle 4^{n}-\prod_{i=1}^{\pi(n)}p_{i}$ 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 $\displaystyle\prod@\slimits@@@_{i=1}^{\pi(n)}p_{i}$ for $0 ValuesOf4nAnddisplaystyleprodi1pinPiFor0N26 2013-03-22 17:04:51 2013-03-22 17:04:51 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Example msc 11N05 msc 11A25 msc 11A41