[QUOTE=cheesehead;185857]But that's a big [I]if[/I].[/QUOTE]No, this is a big [size=30]if[/size].

[size=1][color=#c0c0c0]Sorry for the distraction, but this whole topic is silly so I thought a little bit more silliness can't hurt[/color][/size]

[U]NOW I learn that science_man_88 had already started a new thread ([URL]http://mersenneforum.org/showthread.php?p=185865[/URL]) with essentially the same inquiry![/U] ... and it already has responses with much of the information I posted here.

But science_man_88 didn't bother coming back here to post a note saying so.

And he didn't mention in his new thread that he'd already posted the same inquiry in an existing thread[U], so no one reading the new thread had any reason to think about coming here to post a note, either.
[/U]

Another example is:
31;331;3331;33331;333331;3333331;33333331
All these numbers are prime, however the next number in the series is not: 333333331 = 17 * 19607843

Another one: If you count up from 3, there always seem to be more primes of the form 4n+3 than of the form 4n+1. Sometimes they draw level, but 4n+3 always seems to pull ahead again...until the prime 26861.

I'm an idiot that's obviously what you want to hear

[QUOTE=science_man_88;186276]I'm an idiot that's obviously what you want to hear[/QUOTE]

Maybe some of us, not me of course!

You don't have to be an idiot to say dumb things.

Most of us just hope you are managing to learn something (math and computer stuff that is) from us. If you aren't learning anything then you would be an idiot.

[quote=retina;172949]...Prime95 is not designed to test arbitrary numbers for primeness. Just certain special forms like Mersenne numbers.[/quote]

[quote]A Mersenne number is a number [URL="http://mathworld.wolfram.com/OftheForm.html"]of the form[/URL] M[sub]n[/sub] ? 2[sup]n[/sup] - 1. The Mersenne numbers consist of all 1's in base-2, and are therefore [URL="http://mathworld.wolfram.com/Binary.html"]binary[/URL] [URL="http://mathworld.wolfram.com/Repunit.html"]repunits[/URL]. [/quote]The question mark in the formula represent three horizontal lines, which I take to mean "may be equal to".

The second line was sort of a jaw-dropper, meaning it hit me right off. Any binary number consisting of all 1's is Mersenne.

Below is a link to where I found this:

[URL]http://mathworld.wolfram.com/MersenneNumber.html[/URL]

You are easily impressed.
M[SUB]n[/SUB] ≡ 2[sup]n[/sup] - 1 [I]are[/I] Mersenne numbers.
≡ means [URL="http://mathworld.wolfram.com/Defined.html"]equal by definition[/URL], not "may be equal to", heh?

[URL="http://en.wikipedia.org/wiki/Mersenne_prime"]Mersenne primes[/URL] are only a subset of Mersenne numbers.

Of course, Prime95 is suited for testing [I]all[/I] Mersenne numbers. For those with composite n, it simply returns the answer much sooner than for others. :smile: M[SUB]n[/SUB] is composite if n is composite.

[quote=storm5510;187338] The second line was sort of a jaw-dropper, meaning it hit me right off. Any binary number consisting of all 1's is Mersenne.[/quote]
Consider the base 10 analog: 10^n-1 is all 9's. If we call these numbers, say, 10-Mersennes, then we could say: Any decimal number consisting of all 9's is 10-Mersenne. Compare to your statement regarding binary numbers and Mersennes. Doesn't seem so surprising when it's put that way, does it? :smile:

In reality, I doubt anybody would really care about "10-Mersenne"s because they're never prime and their factorization is simply 9*(base 10 repdigit with all 1's) by definition. To produce a base b repdigit with n 1's, the formula is (b^n-1)/(b-1), e.g. (10^n-1)/9, (10^3-1)/9=999/9=111, (2^n-1)/(2-1)=2^n-1, or 2^3-1=7=111[sub]2[/sub] (meaning 111 in base 2)

Note that the "three horizontal line" symbol, when used in modular arithmetic, means "[URL="http://mathworld.wolfram.com/Congruence.html"]congruent to[/URL]", e.g. 13 ≡ 1 (mod 12).

[QUOTE=Mini-Geek;187358]Note that the "three horizontal line" symbol, when used in modular arithmetic, means "[URL="http://mathworld.wolfram.com/Congruence.html"]congruent to[/URL]", e.g. 13 ≡ 1 (mod 12).[/QUOTE]

Yes, that's fairly standard. "Defined as", by contrast, has used just about every symbol under the sun...

[TEX]:=[/TEX]

[TEX]\stackrel{\tiny\Delta}{=}[/TEX]

[TEX]\stackrel{\tiny\text{def}}{=}[/TEX]

[TEX]\equiv[/TEX]

[TEX]\stackrel{.}{=}[/TEX]

etc.

[quote=Batalov;187342]You are easily impressed.[/quote]

With people, never. Other things, sometimes.