mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2006-03-23, 23:44   #12
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

DA916 Posts
Default

I was asking about positive integer bases: How many zeroes in total in all bases of the largest known Mersenne prime? If you can't answer exactly then please give an educated guess.
paulunderwood is online now   Reply With Quote
Old 2006-03-23, 23:49   #13
Citrix
 
Citrix's Avatar
 
Jun 2003

32×52×7 Posts
Default

Quote:
Originally Posted by Uncwilly
Incorrect. Once you get past the base that is the number itself, you will run out of 0's. Right, Bob?
Wrong answer, you never run out of bases.
Citrix is offline   Reply With Quote
Old 2006-03-24, 00:25   #14
Uncwilly
6809 > 6502
 
Uncwilly's Avatar
 
"""""""""""""""""""
Aug 2003
101×103 Posts

100010101100102 Posts
Default

Quote:
Originally Posted by Citrix
Wrong answer, you never run out of bases.
I understood it Paul's way. No decimals, no negatives. My answer is correct in that manner.
Uncwilly is offline   Reply With Quote
Old 2006-03-24, 00:33   #15
Citrix
 
Citrix's Avatar
 
Jun 2003

32·52·7 Posts
Default

Still incorrect. Learn to count.
Citrix is offline   Reply With Quote
Old 2006-03-24, 00:50   #16
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

13·269 Posts
Default

The maximum base is base M43 which is one digit. No zeroes there.

The first digit is non-zero by definition.

The last digit in any base is not zero because it is prime.

Therefore all two digit representations cannot have any zeroes.

That cuts it down a bit...
paulunderwood is online now   Reply With Quote
Old 2006-03-24, 01:10   #17
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

7678 Posts
Default

Uncwilly's right.
Except for n=0, if you are talking about positive integers represented in positive bases, there will necessarily be no more zeroes for a number n above after base n so the total number of zeroes must be finite.

After base n, the digit itself is n OBVIOUSLY.
grandpascorpion is offline   Reply With Quote
Old 2006-03-24, 02:26   #18
Citrix
 
Citrix's Avatar
 
Jun 2003

157510 Posts
Default

No after M43 it will be the same decimal represntation as M43 not one digit. Think about it.

So since there are infinite bases, there are infinite #'s produding OO 0's.

Citrix
Citrix is offline   Reply With Quote
Old 2006-03-24, 02:27   #19
Citrix
 
Citrix's Avatar
 
Jun 2003

32×52×7 Posts
Default

Quote:
Originally Posted by paulunderwood

The last digit in any base is not zero because it is prime.

Can you prove this?
Citrix is offline   Reply With Quote
Old 2006-03-24, 02:41   #20
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

503 Posts
Default

That's not correct Paul There's an exception. Prime p only has a zero in the first digit if you are writing the number in base p. It would be 10.

If the last digit is zero in base b, it must be a mulitple of b. That's obvious.
10 in base 10 is a multiple of 10. Right? 10 in base 2 is a multiple of 2. Right? Since a prime p's only factor above 1 is p. It can only have a 0 in the unit's digit in it's own base.

Quote:
No after M43 it will be the same decimal represntation as M43 not one digit.
Think carefully about that statement. Decimal representation is only pertinent to base 10. There's a unique zero for each base. Think of hexidecimal notation. Does anyone write 10 in a digit's place for a hex number. No, they write A. You need a unique "character" for each possible digit in a base.

Last fiddled with by grandpascorpion on 2006-03-24 at 02:48
grandpascorpion is offline   Reply With Quote
Old 2006-03-24, 03:21   #21
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

13·269 Posts
Default

You're right on both accounts: M43 is not the maximum base and 10 in base M43 is M43...
paulunderwood is online now   Reply With Quote
Old 2006-03-24, 04:50   #22
Uncwilly
6809 > 6502
 
Uncwilly's Avatar
 
"""""""""""""""""""
Aug 2003
101×103 Posts

2×4,441 Posts
Default

Quote:
Originally Posted by Uncwilly
Once you get past the base that is the number itself, you will run out of 0's.
I stand by this for all natural bases. (note the added emphasis in the quote) Leading zeros are not counted (it is chasing your tail). Those to the right of the units column don't count either, because we are dealing with a whole number. The number is finite, but if it is calculatable is beyond me. I would have to use tools and brute force it.

Last fiddled with by Uncwilly on 2006-03-24 at 04:52
Uncwilly is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
(M48) NEW MERSENNE PRIME! LARGEST PRIME NUMBER DISCOVERED! dabaichi News 571 2020-10-26 11:02
Yes, Virginia, there _is_ a largest prime number! R.D. Silverman Data 82 2013-08-14 15:58
New largest prime number found Prime95 Miscellaneous Math 20 2008-07-29 16:58
get the 15th largest prime number in 3 months wfgarnett3 PSearch 1 2004-06-28 20:51
New largest prime number??? McBryce Lounge 39 2003-08-12 19:35

All times are UTC. The time now is 22:02.

Thu Nov 26 22:02:14 UTC 2020 up 77 days, 19:13, 4 users, load averages: 1.37, 1.52, 1.49

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.