prime95 wrong about prime number:S
 

heey, guys

i just downloaded prime95, to test some numbers on prime.
i first started to test this number: 36894618866352809087 but than it says:"this number is not a prime, no need to test it.", i thought well that could be possible, i started testing other number:
when i test 5 its ok
when i test 9, it says this is not a prime, no need to test.(but it is a prime)
when i test 97 it tests it and says its no prime..wtf:S(also this is a prime)

so now i don't really trust prime with my 36894618866352809087, is there an other version of prime what i can use??

//edit
got prim95 v25,9 build 4

[QUOTE=nielskool;172944]heey, guys

i just downloaded prime95, to test some numbers on prime.
i first started to test this number: 36894618866352809087 but than it says:"this number is not a prime, no need to test it.", i thought well that could be possible, i started testing other number:
when i test 5 its ok
when i test 9, it says this is not a prime, no need to test.(but it is a prime)
when i test 97 it tests it and says its no prime..wtf:S(also this is a prime)

so now i don't really trust prime with my 36894618866352809088, is there an other version of prime what i can use??

//edit
got prim95 v25,9 build 4[/QUOTE][url=http://wims.unice.fr/wims/wims.cgi?session=NX3BE489D1.1&lang=en&cmd=reply&module=tool%2Falgebra%2Ffactor.en&calc=factor&formula=36894618866352809087]36894618866352809087 is not prime.[/url]

9 is not prime! 3x3=?

yea your right 9 isn't, my fault..:S
but 97 is.

Prime95 tests 2^97-1 and correctly informs that it is not prime. Nothing wrong there.

Prime95 is not designed to test arbitrary numbers for primeness. Just certain special forms like Mersenne numbers.

[url]http://www.alpertron.com.ar/ECM.HTM[/url]
[url]http://factorization.ath.cx/search.php[/url]
are good tools for quickly finding the factorizations and/or primality of small numbers

Nielskool, you have misunderstood the purpose of the program, which is to test numbers of the form 2^p-1 for primality. I'm not sure what the limit is for the client, but the GIMPS project currently tracks values of p up to a billion, which corresponds to values of 2*p-1 up to about 300 million digits.

Before testing the number 2*p-1 for primarily, which could take many months, it first checks the number p, which takes just a few microseconds. If p is not prime, then neither is 2^p-1 and there is no need to test the latter.

The number you tried - 36894618866352809087 is not prime. In fact it is 40849 * 903195154504463, but if it had been, then the number 2^36894618866352809087-1 which has more than 11 billion billion digits, is way too large to be tested with the available technology now or in the foreseeable future.

[quote=retina;172947][URL="http://wims.unice.fr/wims/wims.cgi?session=NX3BE489D1.1&lang=en&cmd=reply&module=tool%2Falgebra%2Ffactor.en&calc=factor&formula=36894618866352809087"]36894618866352809087 is not prime.[/URL]

9 is not prime! 3x3=?[/quote]

The link is 404. (Not that it matters anyway.)

Nielskool, Prime95 is not saying that 97 is not prime. It is saying that 2^97-1 = 158456325028528675187087900671 is not prime. It is 11447 * 13842607235828485645766393. BTW, what are you actually trying to do? If all you are doing is testing small numbers for primality, then these can be checked in under a second. It is not hard to test numbers up to 1000 digits either. If they are composite, you will almost certainly know this almost immediately. If you're wanting to factorize them, that's a different problem.

[QUOTE=10metreh;173018]It is not hard to test numbers up to 1000 digits either.[/QUOTE]

But not with Prime95.

if you look at wikipedia the double mersenne primes go:

7, 127, 2147483647, 170141183460469231731687303715884105727
first all of them end in 7
next if you look at the table for mersenne primes they have:

p Mp
3 7
7 127
127 170141183…884105727

If I'm right in assuming the last Mp is the last in this series and this pattern continues( the pattern is Mp becomes the next p) then the next one in this sub series( or what ever you want to call it) is:

p
170141183460469231731687303715884105727

Mp
(2^170,141,183,460,469,231,731,687,303,715,884,105, 727)-1


if this is true it smashes all records as the biggest prime to date and biggest mersenne prime is 2^46 million and something this is 2^ 170 Undecillion and something.


can anybody try testing this one ( oh by the way if all GIMPS computers crash don't be surprised as if I did the right conversion it will take 21 tera tera tera bytes to write out in binary code) I was once a part of gimps but I quit as it was taking too long for my patience.

[QUOTE=nielskool;172944]heey, guys

i just downloaded prime95, to test some numbers on prime.
i first started to test this number: 36894618866352809087 but than it says:"this number is not a prime, no need to test it.",[/QUOTE]

36894618866352809087 = 40849 * 903195154504463

[quote=science_man_88;185825]next if you look at the table for mersenne primes they have:

p Mp
3 7
7 127
127 170141183…884105727

If I'm right in assuming the last Mp is the last in this series and this pattern continues( the pattern is Mp becomes the next p)[/quote]You're referring to a subset of the Mersenne primes.

This subset is in the sequence: [I]2,[/I] 3, 7, 127, ... in which the first member is 2 and each subsequent member is 2[sup](previous member)[/sup]-1. These are called the Catalan-Mersenne numbers in the Wikipedia article [URL]http://en.wikipedia.org/wiki/Double_Mersenne_number[/URL].

Note that Catalan came up with the idea for this sequence in 1876, so it's been looked-at for over a century.

[quote]then the next one in this sub series( or what ever you want to call it) is:

p
170141183460469231731687303715884105727

Mp
(2^170,141,183,460,469,231,731,687,303,715,884,105, 727)-1[/quote]Yes, but no one yet knows whether it is prime ... and it's too big to be tested for primality by any now-known method.

[quote]if this is true[/quote]But that's a big [I]if[/I].

There are many number patterns that seem to make sense for a while, but fail to hold true as the numbers get bigger. This is such a common phenomenon that it has a name: [U]The Strong Law of Small Numbers[/U].

For example, consider the sequence F[sub]n[/sub] = 2[sup]2[sup]n[/sup][/sup]+1.

F[sub]0[/sub] = 3
F[sub]1[/sub] = 5
F[sub]2[/sub] = 17
F[sub]3[/sub] = 257
F[sub]4[/sub] = 65537

The first five (which you may recognize as the Fermat numbers) are all prime.

But the next one, F[sub]5[/sub] = 4294967297, is composite. 4294967297 = 641 × 6700417.

As it says at [URL]http://en.wikipedia.org/wiki/Strong_Law_of_Small_Numbers[/URL]

[quote=Wikipedia]In his humorous 1988 paper [B]The Strong Law of Small Numbers[/B], the mathematician [URL="http://en.wikipedia.org/wiki/Richard_K._Guy"]Richard K. Guy[/URL] makes the statement that "There aren't enough small numbers to meet the many demands made of them." In other words, any given small number appears in far more contexts than may seem reasonable, leading to many apparently surprising coincidences in mathematics, simply because small numbers appear so often and yet are so few. [URL="http://en.wikipedia.org/wiki/Confirmation_bias"]Confirmation bias[/URL] can lead many inexperienced mathematicians to conclude that these concepts are related, which in fact they are not.[/quote]Note the reference to "confirmation bias".

From [URL]http://en.wikipedia.org/wiki/Confirmation_bias[/URL]

[quote=Wikipedia]In [URL="http://en.wikipedia.org/wiki/Psychology"]psychology[/URL] and [URL="http://en.wikipedia.org/wiki/Cognitive_science"]cognitive science[/URL], [B]confirmation bias[/B] is a tendency to search for or interpret new information in a way that confirms one's preconceptions and to irrationally avoid information and interpretations which contradict prior beliefs. Confirmation bias is a type of [URL="http://en.wikipedia.org/wiki/Cognitive_bias"]cognitive bias[/URL] and represents an error of [URL="http://en.wikipedia.org/wiki/Inductive_reasoning"]inductive inference[/URL], or as a form of [URL="http://en.wikipedia.org/wiki/Selection_bias"]selection bias[/URL] toward confirmation of the hypothesis under study or disconfirmation of an alternative hypothesis.[/quote]Back to your post:

[quote=science_man_88]it smashes all records as the biggest prime to date[/quote]Wouldn't that be nice and exciting!

There are lots of things that would be nice and exciting [I]if they were actually true[/I]. But, as explained (humorously, but with truth) in the article on the Strong Law of Small Numbers, there are more possible nice-and-exciting sequences starting with small numbers than can possibly stay true when the sequences are extended to larger numbers.

[quote]can anybody try testing this one[/quote]No, it's too big to be tested by any known method at present.

[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.

[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]

False. Any binary repunit with a [b]prime[/b] number of bits is Mersenne.

[QUOTE=R.D. Silverman;187385]False. Any binary repunit with a [b]prime[/b] number of bits is Mersenne.[/QUOTE]

According to Wikipedia, both definitions are used:

[quote=Wikipedia]In mathematics, a Mersenne number is a positive integer that is one less than a power of two. Some definitions of Mersenne numbers require that the exponent n be prime.[/quote]

[QUOTE]False. Any binary repunit with a [B]prime[/B] number of bits is Mersenne. [/QUOTE]

depend on how you define a mersenne number,id define it as 2^n-1,where n is any positive integer.