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The largest prime number has been located and carries a $100,000 prize

Restrictive prime numbers are numbers of the typep^2-1where the power P is also a prime number

Marin Marsan
Marin Marsan

Researchers on behalf of the Internet Association for Finding Magnificent Prime Numbers (GIMPS), apparently discovered the 45th prime number and thus set a world record.

The Internet Association for Finding Mascenic Prime Numbers announced this week that a computer reported to their server about finding a Mascenic Prime Number.

Restrictive prime numbers are numbers of the type p^2-1 where the power P is also a prime number.

A Marseni prime number is so rare that the computerized search process may take months or even years. An integrity check for the number 45 will last about three weeks and at the end, the approved finder may be entitled to $100,000 from the Electronic Front Fund.

Marin Marsan, after whom the Martian numbers are named, was a 17th century French monk, philosopher, theologian, mathematician, music theorist and scientist who contributed to the theory of numbers with his discovery.

The internet association for finding restrictive prime numbers is based on a community distributed calculation in which anyone who wants to (and has a powerful enough computer), can take part in analyzing and locating restrictive numbers. The 44th prime number was discovered in September 2006 by two researchers from the University of Central Missouri, and included 9.808358 million digits.

Yael Petar

Yael Petar

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55 תגובות

  1. Yehoram:
    Of course you are right.
    I assume that the problem stems from problems in the site's editing program (try writing formulas here and you will see how difficult it is to make what you wanted to be displayed actually be displayed).
    Note that the previous commenters did not notice the error at all and yet understood exactly which numbers were involved.
    The thought creeps into my heart that in a previous version of the editing program the exact same input was displayed correctly and some change in the version of the editing program changed the result.

  2. P^2 -1 is an even number for every P that is different from 2.

    Probably the reference was to 2 to the power of P and not to P to the power of 2.

  3. In the news published by Yael Petar, we found the largest Marsan number (the 45th in the number)
    in September 2008
    : According to your suggestion, I went to the website talking about Marsan numbers and found the following news

    October 20, 2008:
    New GIMPS Server goes online
    New client software available
    47th Known Mersenne Prime Found!
    Verification in progress.

    This information requires updating your information

  6. Well - here too it went a little wrong because the first 2 were replaced with the fractions, but I hope it's understandable anyway.

  7. In section 2, the word order has changed a bit.
    I will try to rewrite the words in the hope that it will not change again.
    Should be "because except 2" and not "except 2 because"

  8. Gustav:
    No bullshit, but you won't be surprised to know that there are much better ways to do the job.
    There is no point in going into detail right now, but consider the following:
    1. The number of ones - as explained - should be prime itself - there is no need to check for numbers consisting of a number of ones that is not prime.
    2. There is no point in dividing by even numbers other than 2 because all the first ones are not even.
    3. In fact, there is no point in trying to divide by numbers that are not prime because every odd number is divisible by the prime.
    4. There is no point in trying to divide by numbers that are larger than the root of the number because when a number is presented as a product of two other numbers - one of them is always smaller than the root or equal to it.
    5. All of the above is only the tip of the iceberg. There is a polynomial algorithm for checking primality (and we will not go into the definition of the term polynomial right now except that it is said to be much more efficient when it comes to really large numbers).

  9. Tamm's question (very tame!): Would a possible technique for finding prime numbers from Resen be, therefore, to let the computer progress in a loop of binary numbers that all consist of 1, translate them into decimal and then check if they meet the condition?
    In other words, would such an algorithm work? Just for fun, I initially thought about the simple loop that looks for primes (each number in the loop is tried to divide without a remainder by 2, 3, 4, and so on until a divisor is found, and if not - then we have a prime) and then on each prime that is found, a check is made to see if it is prime . Then I thought to check only the binaries that only consist of 1.
    Am I in the right direction, or am I talking nonsense?

  10. By the way, Mersen in the picture above looks like he was caught in the act...or is what he is holding there in his hand not what I think?

  11. Good evening my dears, I checked the topic and it's all nonsense in strawberry banana juice, I got to the initial marsani number 69 and there the joke that caused the eruption of the big bang is revealed, after which the one-legged dinosaurs and testicular triangles skipped to their pleasure with Yaron London and his learned friends.
    In short, stop talking nonsense, what you smoke is not good for you.
    Or as Herzl said in his fine time: "Hammelblablallalshadgaldalgalal!!!".
    Yes, geniuses like you will multiply, multiply and multiply and fill the whole land!
    May you have a happy new year, a happy holiday and an easy and kosher fast.

  12. And it will read in the other book - about the laws of the broken mirrors and abuses:

    "The Sonata
    To Hogin..the wonderful Swiss"-for advanced students only.

    With the blessing of enlightenment..to the acceleration particle.
    Munin and Odin/to the tribes of Israel - and Judah...

    (Don't forget Marin Marsan's numbers - for beginners, of course)

  13. Dear sonnet!

    You are right in at least some of your words, and my heart, my heart, to the plot of your tassels becoming carbonized!, there is no doubt that Hagen exaggerated her burning reaction, but, dear Mr. Sonnet, let us be forgiving to the girls of the fair sex commenting here and don't be angry with us for worrying about their beautiful tassels, more than the concern for your burning tassels (although all the pain you rightly feel)

    So have a good day
    with a smile
    And please don't get angry
    Sabdarmish Yehuda

  14. Sabdarmish - what are you buying? How many times did she patronize you? Only spineless people will find wisdom in obscure language.
    To strengthen my claims, see responses 18, 20, and 37; Comment 18 says it all (or nothing.)
    In short, unnecessary noise.
    attache:
    * I was educated: Rabbi is...
    * The mileage on the site: number of years...
    * "Your charred tassels" -?!

  15. To the sonnet master
    Your perverted approach to our Hugin, inspires you more than any average knowledgeable commenter.
    Only uneducated people would define my words of wisdom as vague language.
    Your form of expression is not what is accepted here on the site.
    Good night
    Sabdarmish Yehuda

  16. To the sonnet master
    With reference to your rant, did you decide to represent the council of foils in a mocking way??
    You better learn a lot more, before you mock.
    Check your charred tassels, before you decide what is acceptable here.

  17. I don't know about you, but the comments of Miss "Hugin and Monin.. of Odin.." usually seem stupid and irrelevant to me (certainly not intelligent enough to give her another platform...). It is very possible that this is a troll?! (Even the news, and certainly the vague language, don't really go well with what is accepted here on the site)

  18. Avi. A proposal to upgrade the site - check the possibility of including chat on the site
    It seems to me that there is a lot of restrained energy here, almost at the core (the new accelerator site)

  21. You are right Arie, and for the sake of good order I will quote the relevant passage from Wikipedia:-

    In mathematics, a Mersenne number is a number that is one less than a power of two,

    Mn = (2^n)- 1.

    A Mersenne prime is a Mersenne number that is a prime number

    That is, Marsan's number is (2 to the power of P) minus 1, where P is prime.
    If the resulting Marsan number is prime then the number will be called a prime Marsan number.
    For example :-
    Let's take a prime number N=3, two to the power of N is 8, subtract one and get 7. 7 is a prime number but 7 is also a prime prime number.
    On the other hand, we will take N=11, two to the power of 11 is 2048, minus 1 we will get 2047.
    2047 is a Mersen number, but it is not a prime Mersen number, because 2047=23*89,
    So it's good that Aria enlightened our eyes to the problem, and from now on we'll be precise, the Marsan books that catch are the first Marsan books and today we will find the 45th number in the series.

    good evening
    Sabdarmish Yehuda

  22. I comment because it hindered my understanding until I solved the matter.
    As all readers and commenters know (and I didn't know or remember this when I first read the article and the comments) a Mersen number is any number of the form n^2 – 1, while the article talks about prime Mersen numbers.
    Both in the title and in some of the comments it says just a number from Marsan (without a score - initial).
    So it may be obvious to those in the know regarding this article, but accuracy is important for the benefit of those who don't know so much.

  23. to the cool responder
    Don't pretend to be cool, dear, after all, only Hugin was added to us from the fair sex, and you received Yael Yalet Hahan.
    I think that's pretty fair.

    sweet Dreams
    Sabdarmish Yehuda

  26. Leshi HaCohen
    We will think about an article that will at least shake some paradigms (Newton, dark mass, etc.).

    And dear Michael-
    Did you notice that we were named…. together!
    Of course, there is nothing to compare, I - Judah, and you and the rest - "others".
    Allow me to enjoy a few moments of glory until you and..the "others" respond.

    I ask you, and the "other" commenters to respond gently in my beautiful time.

    Wonderful day!
    Sabdarmish Yehuda

  28. Judah and others!
    I've been reading the site for months and have come across many comments from you, from Hogin, Michael and Ami Bachar, Higgs and a few other very smart guys. You too write articles and articles, etc., about the things you have to say. It's really interesting to me and I think others will also read enriching, sharp and intelligent information!
    I also really like to read Dr. Nachmani and Rosenthal. Ran Levy should write more.
    A site for intelligentsia 🙂

  29. Sabdarmish Yehuda
    If anything, if only to the question why is the task so heavy?
    In a rough calculation using different debugging methods, the number of calculations is about N log n
    As I imagine, for each additional bit, which is approximately the number of digits times the number itself, calculation operations are performed for each additional bit in the chain. Think for yourself, this is a lot of work even if you divide it into several computers at the same time.

  31. To Judah
    Come and help you simplify a little more for those who need it
    Restraint and hold numbers are represented in binary in computer memory as a string of bits that are all in the ON state
    i.e. 32,582,657 thirty-two million etc. bits (on) 1111111…… Unity and such is every number from Rein. That is, the number of digits is the number itself in this representation.
    In the transition from the binary system to the decimal system, this is about a third of the number of digits.
    And finally the number 44 occupies about four megabytes in the computer's memory. And when nowadays a personal computer
    That you buy in the supermarket comes with an internal memory of at least 1 gigabyte, that is 250 times the length of the number. This is also the reason that a home computer is able to handle calculations of this type.
    Hope it was simple enough and that there aren't too many spelling and syntax errors.

  32. meet
    The formula you gave does not stand the test of reality even with small numbers.
    For example:- Mersen number number 12 is built from the initial number 127 and contains 39 digits, while the Mersen number that follows has a big jump and is built on the initial number 521 and already contains 157 digits. There is no way that such a large difference between the two consecutive numbers could be expressed in your formula.
    I suggested, which I read on one of the websites about Marsan numbers, to write Marsan numbers according to base 2 and not according to decimal base. In this way, Marsan numbers will be registered with only a few.
    For example: 3 is equal to 11 according to base 2,
    7 is equal to 111 according to base 2,
    31 is equal to 11111 according to base 2, etc.
    So there is no need to go through all the decimal digits and you only have to check the binary form as I explained. A small savings.
    You can see more explanations on the website that Michael sent me:-

    http://en.wikipedia.org/wiki/Mersenne_prime

    Well Michael, do you feel like I did my homework with the site you sent me to?

    Good Day
    Sabdarmish Yehuda

  34. meet
    Regarding the 44th Mersen number:-
    (2 to the power of 32,582,657 ) minus 1 will give you exactly a number with 9,808,358 digits.

    Regarding the formula you brought - I believe it can be improved so that in the high numbers it will give less

    Good night
    Sabdarmish Yehuda

  35. 32,582,657 is the 44th Marsan number? If so, it does not include 9 million digits as written in the article.

    From the sequence of numbers that gave a point, I did an exponential extrapolation and pretty soon it turns out that the next number or the following consecutive numbers will be =
    Y=1.7021*e^0.3941x

    where X is the serial number of the Mersen number and Y is approximately its value. At the low values ​​it works great. at less high altitudes.

    Let's make some attempts:

    Let's say, what is the 20th Marsan number?
    From the formula we get 4509 while the real number is 4423

    The calculated tenth number is 87 while the real number is 89.

    The number 36 would be approximately 2,469,343 according to the formula, while its true value is 2,976,221

    The 44th number that is calculated is 57,786,328 while the real number is 32,582,657. This is already a very big exception

    It seems that from the 40th and above the Mersen numbers do not progress exponentially or at the very least (due to a lack of points) the exponent in them changes dramatically.

    Perhaps estimates of this kind can facilitate blind calculations of the next chronological number calculation?

  37. The United States
    There is a close connection between Mersen numbers and computers in general.
    Because all Marsan numbers are actually a binary bit chain with all bits in the ON state
    ie a bit string of "1"
    where the length of the chain expresses the exact number
    This is probably also the reason why the award was given to the residents of the computer funds by the electronic bra

  38. A thought that also occurred to me, there may be some allusion here to the results of some upcoming discoveries,
    Well, this is just a hypothesis, because there is a combination of strange and questionable scenarios here..

  39. It is not always possible to answer the question of usability in advance.
    I am not currently aware of any practical uses of Mersen numbers but, beyond the fact that there may be uses that I am not aware of, there is always the possibility that someone will find a use for these numbers in the future.
    By the way - I noticed that the sentence Nir mentioned also appears in the first link I provided and it even points to the second link.

  40. The question remains - are the above numbers important?, because it seems that they are just for mathematical fun (although it is sometimes possible to earn a hundred thousand dollars)
    good evening
    Sabdarmish Yehuda

  41. Nir:
    This is true as you can see here:
    http://en.wikipedia.org/wiki/Perfect_numbers
    Pep, I sent Galileo a response to an article published there on the subject of vampire numbers and I also showed a connection between their groups and Marsan numbers, but it's just a curiosity because in my opinion, vampire numbers are really of no importance (and I also wrote this to them in my response).

  42. Restrained prime numbers are related to perfect numbers (those whose sum of parts is equal to themselves). You get a perfect number by the formula: 2 to the power of (p minus 1) times (2 to the power of p minus 1) where p is taken from the list of "dots" above, so that the first multiple is prime from the curb...
    As far as I remember all known perfect numbers are of this form, and there is a mathematical theorem that every even perfect number is of this form.

  44. To Michael
    Thanks for the link to the site. Now everything is clear.
    Sometimes you are… (I'm looking for the words)… nice.

    Good Day
    Sabdarmish Yehuda

  46. There is a famous conjecture that there are an infinity of Mersen numbers (Mersen himself was apparently mistaken when his hair was upside down...).

  49. 2 3 5 7 13 17 19 31 61 89 107 127 521 607 1,279 2,203 2,281 3,217 4,253 4,423 9,689 9,941 11,213 19,937 21,701 23,209 44,497, 86,243 110,503 132,049 216,091 756,839 859,433 1,257,787 1,398,269 2,976,221 3,021,377 6,972,593 13,466,917 20,996,011 24,036,583 25,964,951 30,402,457 32,582,657 XNUMX

  50. Can someone give the list of the first Marsan numbers so we can see what it is?
    Is it about:-
    3, 7, 31, 127, etc.?

    Good Day
    Sabdarmish Yehuda

  51. Mersen's prime numbers are obtained by
    2 to the power of prime p minus 1

    Why not try to get an initial number - we will call it "initials of science"
    7 to the power of a prime number minus 1
    And we will offer a reward for the straight finisher.
    Which, by the way, should have enough space on the computer to store a number with a lot of digits (much more than 9 million).

    : )

  52. Marsan numbers are very important in number theory, closely related to prime numbers. and have very interesting features.

    for example:
    An interesting question in number theory is, does there exist a Marsan number whose factors (decomposition into prime factors) do not contain multiplication (that is, the same prime factor that appears at least twice). The accepted opinion is that there is no such thing as a number from Marsan. But there is no proof of that.

  54. Ami Bachar,

    Mathematics serves physics, and physics serves man.

    at the general level-
    The more we explore mathematics, the more tools we will have to explain natural phenomena. The theories will be more elegant.

    And on a practical, specific level - it seems to me that the study of prime numbers is used a lot in computer science - encryption and random codes.

    There are many unsolved questions in mathematics, and research like the one presented in the article strengthens or weakens the claims that underlie these questions.

  55. What is good for?
    Computing power, electricity, processing time, components... What do you do with restrictive numbers and what is expected to be done with the number 45 that could not be done with the number 44? Is there an essential need for the number 46?

    Anecdotally, as an article for the science website, I understand the passage. But if there really is no meaning (except for the American need to increase and increase and increase) then this is an embarrassing, wrong and stupid matter.

    Greetings friends,
    Ami Bachar

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