Number of factors

JohnFullspeed · 2011-07-19, 12:28

Is there a way to ow howman priimes factor MAXIMUM can have a value

For exemple ea value with 20 digits can hava how many primes facctor

The diggits number, the root....
Thanks

Gammatester · 2011-07-19, 12:55

$[\log_2(n)]$ if your number is n, i.e. for a 20 decimal digit number $[\log_2(10^{20}-1)] = 66$ . If you want different prime factors, search the largest product of the first primes that is <= n and count the factors:

10^20-2*3*5*7*11*13*17*19*23*29*31*37*41*43*47*53 > 0
10^20-2*3*5*7*11*13*17*19*23*29*31*37*41*43*47*53*59 < 0

Therefore you can have a maximum of 16 different prime factors.

JohnFullspeed · 2011-07-19, 15:03

Thanks

It was just to set the size of and array...
John

2011-07-19, 12:28	#1
JohnFullspeed May 2011 France 7·23 Posts	Number of factors Is there a way to ow howman priimes factor MAXIMUM can have a value For exemple ea value with 20 digits can hava how many primes facctor The diggits number, the root.... Thanks

2011-07-19, 12:55	#2
Gammatester Mar 2009 2×19 Posts	$[\log_2(n)]$ if your number is n, i.e. for a 20 decimal digit number $[\log_2(10^{20}-1)] = 66$ . If you want different prime factors, search the largest product of the first primes that is <= n and count the factors: 10^20-2357111317192329313741434753 > 0 10^20-235711131719232931374143475359 < 0 Therefore you can have a maximum of 16 different prime factors. Last fiddled with by Gammatester on 2011-07-19 at 13:12*

2011-07-19, 15:03	#3
JohnFullspeed May 2011 France 7×23 Posts	Prrimess Factor Thanks It was just to set the size of and array... John Last fiddled with by JohnFullspeed on 2011-07-19 at 15:03

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