Estimate number of spam emails, in thousands.

2007-06-22, 12:10

Predict number of digits in smaller factor of $2^1^0^6^1-1$

My prediction: 70 to 79

Xyzzy · 2007-06-22, 12:37

Quote:

Predict number of digits in $2^1^0^6^1-1$

$ echo '2^1061-1' | bc | tr -d '\\\n' | wc -c
320

VolMike · 2007-06-22, 13:26

Quote:

Posts: ∞
Join Date: Aug 2002

http://mersenneforum.org/images/icons/icon1.gif
Quote:
Predict number of digits in http://mersenneforum.org/cgi-bin/mim...%5E0%5E6%5E1-1
$ echo '2^1061-1' | bc | tr -d '\\\n' | wc -c
320

This number is composite

Xyzzy · 2007-06-25, 00:21

Quote:

This number is composite

Of course it is. But, 2¹⁰⁶¹-1 is always going to be:

Code:

24707306311927565716857342128774085333197833223161879682238935306082\
80512304630699364750777605433648622889134085898582902707626188791424\
27816178466724534313869039824556355421587484018239859883229052450779\
38567513252198179128990807936780194781391547404884040101606295111368\
825026273254703636026307207764436438929167613951

Disclaimer: The OP revised their question after we posted our first response.

VolMike · 2007-06-26, 13:27

Thus , the result should be 1, becouse it is the smallest factor of 2^1061-1 :)

2007-06-26, 15:19

Smaller prime factor.
Should I be very accurate?

garo · 2007-06-26, 22:24

The word you are looking for starts with a p and has 11 digits.

2007-06-29, 18:50

Don't understand.

Quote:

Originally Posted by garo

The word you are looking for starts with a p and has 11 digits (not letters).

What do you mean?

I don't get it.
Can you say what it is.

jasonp · 2007-07-03, 03:45

Quote:

Originally Posted by lazy

I don't get it.
Can you say what it is.

A penultimate (a fancy word for 'second to last') factor refers to the second-largest factor of a number. The size of this factor is what people use to classify how difficult the number was to factorize. E.g. if the largest factor was 1000 digits and the penultimate factor was 30 digits, your factorization is not very noteworthy.

2007-07-03, 12:24

Yes, it is

So, But the chance that it has upto 3 prime factors is rare. Like M751 or M811.
If so, I didn't mean the penultimate prime factor,
but the smaller prime factor.

Even if it has 2 prime factors, the penultimate factor means the larger prime factor, and not the penultimate prime factor.

If it has 3 prime factors, I mean the smaller prime factor always.
The penultimate factor means here the product of larger two prime factors.
It is again, not also the penultimate prime factor.

ewmayer · 2007-07-03, 18:08

Quote:

Originally Posted by lazy

So, But the chance that it has upto 3 prime factors is rare.

No, it's not.

Quote:

Like M751 or M811.

We won't know whether it's like these 2 until we factor it.

Quote:

If so, I didn't mean the penultimate prime factor, but the smaller prime factor.

Better known as "the penultimate prime factor".

Quote:

Even if it has 2 prime factors, the penultimate factor means the larger prime factor, and not the penultimate prime factor.

Wrong.

Quote:

If it has 3 prime factors, I mean the smaller prime factor always.

"Smaller of the three" is nonsensical. Do you mean the smallest?

Quote:

The penultimate factor means here the product of larger two prime factors.

No, that's the "remaining composite cofactor."

Quote:

It is again, not also the penultimate prime factor.

This is again, wrong. Care to try for 0 for 8?

Well-chosen user name, BTW.

View Poll Results: Estimate number of spam emails, in thousands.
Less than 60	0	0%
60 to 69	1	6.67%
70 to 79	2	13.33%
80 to 99	5	33.33%
More than 100	7	46.67%
Voters: 15. You may not vote on this poll

2007-06-22, 12:10	#1
lazy 2×29×107 Posts	Predict number of digits in smaller factor of $2^1^0^6^1-1$ My prediction: 70 to 79 Last fiddled with by lazy on 2007-06-22 at 12:47

2007-06-26, 13:27	#5
VolMike Jun 2007 Moscow,Russia 133₁₀ Posts	Thus , the result should be 1, becouse it is the smallest factor of 2^1061-1 :) Last fiddled with by VolMike on 2007-06-26 at 14:02

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2007-06-26, 15:19	#6
lazy 339₁₆ Posts	Smaller prime factor. Should I be very accurate?

2007-06-26, 22:24	#7
garo Aug 2002 Termonfeckin, IE 5314₈ Posts	The word you are looking for starts with a p and has 11 digits.

2007-07-03, 12:24	#10
lazy 2045₁₆ Posts	Yes, it is So, But the chance that it has upto 3 prime factors is rare. Like M751 or M811. If so, I didn't mean the penultimate prime factor, but the smaller prime factor. Even if it has 2 prime factors, the penultimate factor means the larger prime factor, and not the penultimate prime factor. If it has 3 prime factors, I mean the smaller prime factor always. The penultimate factor means here the product of larger two prime factors. It is again, not also the penultimate prime factor.