Predict number of digits in smaller factor of [tex]2^1^0^6^1-1[/tex]

My prediction: 70 to 79

[quote]Predict number of digits in [tex]2^1^0^6^1-1[/tex][/quote][FONT=Courier New]$ echo '2^1061-1' | bc | tr -d '\\\n' | wc -c
320

:unsure:
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[QUOTE]
Posts: ∞
Join Date: Aug 2002

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Quote:
Predict number of digits in [IMG]http://mersenneforum.org/cgi-bin/mimetex.cgi?2%5E1%5E0%5E6%5E1-1[/IMG]
[FONT=Courier New]$ echo '2^1061-1' | bc | tr -d '\\\n' | wc -c
320[/FONT][/QUOTE]
This number is composite

[quote]This number is composite[/quote]Of course it is. But, 2[sup]1061[/sup]-1 is always going to be:

[code]24707306311927565716857342128774085333197833223161879682238935306082\
80512304630699364750777605433648622889134085898582902707626188791424\
27816178466724534313869039824556355421587484018239859883229052450779\
38567513252198179128990807936780194781391547404884040101606295111368\
825026273254703636026307207764436438929167613951[/code]

:wink:

[SIZE=1]Disclaimer: The OP revised their question after we posted our first response.[/SIZE]

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

Smaller prime factor.
Should I be very accurate?

The word you are looking for starts with a [B]p[/B] and has [I]11[/I] digits.

Don't understand.

[QUOTE=garo]
The word you are looking for starts with a [B]p[/B] and has [I]11[/I] digits (not letters).
[/QUOTE]
What do you mean?

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

[QUOTE=lazy;109318]
I don't get it.
Can you say what it is.[/QUOTE]
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.

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.

[QUOTE=lazy;109516]So, But the chance that it has upto 3 prime factors is rare.[/QUOTE]

No, it's not.

[QUOTE]Like M751 or M811.[/QUOTE]

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.[/QUOTE]

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.[/QUOTE]

Wrong.

[QUOTE]If it has 3 prime factors, I mean the smaller prime factor always.[/QUOTE]

"Smaller of the three" is nonsensical. Do you mean the small[b]est[/b]?

[QUOTE]The penultimate factor means here the product of larger two prime factors.[/QUOTE]

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

[QUOTE]It is again, not also the penultimate prime factor.[/QUOTE]

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

Well-chosen user name, BTW.