Bit level

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Since Mersenne numbers are by nature binary, it makes sense to perform calculations on them directly in binary. When searching for factors of Mersennes Prime95 and some other factoring programs use and report bit level as starting and stopping points, bit meaning binary digit, others use the k value.

Every number can be represented in either binary or decimal. For each new digit added to a number binaries are twice as large, while decimals are ten times as large. A number that has 70 binary digits (all 1's) would be at the 70 bit level. To check for factors from one bit level to the next (e.g. from 70 to 71) takes twice as much work (there are two times as many potential factors to check.)

While at first bit level may appear to be quantum in nature, bit levels such as 75.3 are often seen.

Examples

Binary Decimal Bit level
1111 1111 1111 1111 65,535 16
1 0000 1001 0011 0010 67,890 16.05
1 1111 1111 1111 1111 131,071 17
1010 1010 1010 1010 1010 1010 1010 1010 2,863,311,530 31.42
1111 1111 0000 0000 0000 0000 0000 0000 4,278,190,080 31.99