How much digit in the M?
 

How much digit in the M. Where I can find the formula?

For example. I know that M332192831 is more then 100M digit. But what exact quantity?


[SIZE="1"]Sorry for my English :redface:[/SIZE]

332192831 * log[sub]10[/sub](2) ~= 100M

[QUOTE=Lorenzo;227007]How much digit in the M. Where I can find the formula?

For example. I know that M332192831 is more then 100M digit. But what exact quantity?
[/QUOTE]

M332192831 has 100000007 digits.

The formula (as said): [exponent*log(2)+1] -> "[x]" means round up to next natural number.

retina, kar_bon
Thank you.

[QUOTE=kar_bon;227013]M332192831 has 100000007 digits.

The formula (as said): [exponent*log(2)+1] -> "[x]" means round up to next natural number.[/QUOTE]

according to wikipedia's digits for M your formula would be off by 1.

[QUOTE=science_man_88;227017]according to wikipedia's digits for M your formula would be off by 1.[/QUOTE]There are no fractional digits. You must have whole digits. If the calculation retutrns 100,000,000.0000000003 (with all being sig. fig's, then the number has 100,000,001 digits.

note: Wikipedia is not the tables of stone that came down from the mountain.

Example:

log[sub]10[/sub] (2[sup]43112609[/sup]) + 1 = 43112609 * log[sub]10[/sub](2) + 1 = 12978189.500333

So this number got 12978189 digits.

[quote=kar_bon][exponent*log(2)+1] -> "[x]" means round up to next natural number[/quote]

I think rounding down might work better...

[QUOTE=10metreh;227023]Dropping the "+1" might help.
(Or else change "up" to "down")[/QUOTE]

Yeah, in German it's called 'abrunden', simliar to "up-round" (round down) :grin: (opposite to "aufrunden" -> round up)

[QUOTE=Uncwilly;227021]There are no fractional digits. You must have whole digits. If the calculation retutrns 100,000,000.0000000003 (with all being sig. fig's, then the number has 100,000,001 digits.

note: Wikipedia is not the tables of stone that came down from the mountain.[/QUOTE]

I mean't before rounding and even after rounding it would throw it off by 1.
I never stated that but last i checked digits (m) was define properly there for the mersenne prime table hence I checked it against it.

[QUOTE=kar_bon;227024]Yeah, in German it's called 'abrunden', simliar to "up-round" (round down) :grin:[/QUOTE]
That will likely confuse folks even more (I presume that's what you're grinning asbout) ... So let's try to clarify: 'ab' may *sound* superficially like the English 'up', but it really means down, as in "Abgrund" (literally 'downground", meaning abyss) or "Absturz" (crash or collapse).

Easdier for non-German-speakers to remember by way of the alliterative pair "auf und ab" (up and down).

'Ab' can also be used in the sense of 'away', e.g. 'ableiten', to conduct away, that is, to divert.