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Posted 12 years ago. 39,100. and 17 goes into 17. Hereof, Is 1 a prime number? \(49\) is divisible by \(7\), and from the property of primes it is enough information to conclude that the number is not prime. So it is indeed a prime: \(n=47.\), We use the same process in looking for \(m\). A Mersenne prime is a prime that can be expressed as \(2^p-1,\) where \(p\) is a prime number. Direct link to martin's post As Sal says at 0:58, it's, Posted 10 years ago. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. And maybe some of the encryption Asking for help, clarification, or responding to other answers. 1 is divisible by only one In order to develop a prime factorization, one must be able to efficiently and accurately identify prime numbers. When using prime numbers and composite numbers, stick to whole numbers, because if you are factoring out a number like 9, you wouldn't say its prime factorization is 2 x 4.5, you'd say it was 3 x 3, because there is an endless number of decimals you could use to get a whole number. Very good answer. Sanitary and Waste Mgmt. How many numbers in the following sequence are prime numbers? What I try to do is take it step by step by eliminating those that are not primes. Not 4 or 5, but it There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97. 720 &\equiv -1 \pmod{7}. 6= 2* 3, (2 and 3 being prime). the answer-- it is not prime, because it is also Anyway, yes: for all $n$ there are a lot of primes having $n$ digits. You just have the 7 there again. Those are the two numbers video here and try to figure out for yourself While the answer using Bertrand's postulate is correct, it may be misleading. Given a positive integer \(n\), Euler's totient function, denoted by \(\phi(n),\) gives the number of positive integers less than \(n\) that are co-prime to \(n.\), Listing out the positive integers that are less than 10 gives. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. divisible by 5, obviously. Is it correct to use "the" before "materials used in making buildings are"? The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. The term reversible prime may be used to mean the same as emirp, but may also, ambiguously, include the palindromic primes. The LCM is given by taking the maximum power for each prime number: \[\begin{align} Can you write oxidation states with negative Roman numerals? View the Prime Numbers in the range 0 to 10,000 in a neatly formatted table, or download any of the following text files: I generated these prime numbers using the "Sieve of Eratosthenes" algorithm. I'm not entirely sure what the OP is trying to ask, or exactly what the mild scuffle in the comments is about (and consequently I'm not sure what the appropriate moderator reaction is). For instance, for $\epsilon = 1/5$, we have $K = 24$ and for $\epsilon = \frac{1}{16597}$ the value of $K$ is $2010759$ (numbers gotten from Wikipedia). When the "a" part, or real part, of "s" is equal to 1/2, there arises a common problem in number theory, called the Riemann Hypothesis, which says that all of the non-trivial zeroes of the function lie on that real line 1/2. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. One can apply divisibility rules to efficiently check some of the smaller prime numbers. And what you'll divisible by 1 and 4. How many primes are there less than x? Two digit products into Primes - Mathematics Stack Exchange Answer (1 of 5): [code]I think it is 99991 [/code]I wrote a sieve in python: [code]p = [True]*1000005 for x in range(2,40000): for y in range(x*2,1000001,x): p[y]=False [/code]Then searched the array for the last few primes below 100000 [code]>>> [x for x in range(99950,100000) if p. The original problem originates from the scheme of my local bank (which I believe is based on semi-primality which I doubted to be a weak security measure). In an examination of twenty questions, each correct answer carries 5 marks, each unanswered question carries 1 mark and each wrong answer carries 0 marks. Are there primes of every possible number of digits? For example, 2, 3, 5, 13 and 89. Find the cost of fencing it at the rate of Rs. For example, you can divide 7 by 2 and get 3.5 . For example, the first occurrence of a prime gap of at least 100 occurs after the prime 370261 (the next prime is 370373, a prime gap of 112). If you have only two \phi(3^1) &= 3^1-3^0=2 \\ This should give you some indication as to why . There are other methods that exist for testing the primality of a number without exhaustively testing prime divisors. But remember, part Direct link to Victor's post Why does a prime number h, Posted 10 years ago. If \(n\) is a power of a prime, then Euler's totient function can be computed efficiently using the following theorem: For any given prime \(p\) and positive integer \(n\). Sign up to read all wikis and quizzes in math, science, and engineering topics. RSA doesn't pick from a list of known primes: it generates a new very large number, then applies an algorithm to find a nearby number that is almost certainly prime. allow decryption of traffic to 66% of IPsec VPNs and 26% of SSH The first 49 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, and 227. what encryption means, you don't have to worry (In fact, there are exactly $180,340,017,203,297,174,362$ primes with $22$ digits.). 2^{90} &\equiv (16)(16)(74)(4) \pmod{91} \\ How many semiprimes, etc? Actually I shouldn't I left there notices and down-voted but it distracted more the discussion. at 1, or you could say the positive integers. you a hard one. another color here. If this version had known vulnerbilities in key generation this can further help you in cracking it. [10], The following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents p. As of 2022[update], there are 51 known Mersenne primes (and therefore perfect numbers), the largest 17 of which have been discovered by the distributed computing project Great Internet Mersenne Prime Search, or GIMPS. of them, if you're only divisible by yourself and How many prime numbers are there (available for RSA encryption)? Prime and Composite Numbers Prime Numbers - Advanced Prime Number Lists. Given an integer N, the task is to count the number of prime digits in N.Examples: Input: N = 12Output: 1Explanation:Digits of the number {1, 2}But, only 2 is prime number.Input: N = 1032Output: 2Explanation:Digits of the number {1, 0, 3, 2}3 and 2 are prime number. irrational numbers and decimals and all the rest, just regular On the other hand, it is a limit, so it says nothing about small primes. \(51\) is divisible by \(3\). of factors here above and beyond In fact, it is so challenging that much of computer cryptography is built around the fact that there is no known computationally feasible way to find the factors of a large number. What video game is Charlie playing in Poker Face S01E07? Direct link to eleanorwong135's post Why is 2 considered a pri, Posted 10 years ago. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2p 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 22 1. 1 and by 2 and not by any other natural numbers. Jeff's open design works perfect: people can freely see my view and Cris's view. But as you progress through Bertrand's postulate (an ill-chosen name) says there is always a prime strictly between $n$ and $2n$ for $n\gt 1$. eavesdropping on 18% of popular HTTPS sites, and a second group would Weekly Problem 18 - 2016 . I'll circle the In some sense, 2 % is small, but since there are 9 10 21 numbers with 22 digits, that means about 1.8 10 20 of them are prime; not just three or four! just so that we see if there's any It only takes a minute to sign up. it down anymore. Well actually, let me do Ans. What is the harm in considering 1 a prime number? Then. The question is still awfully phrased. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. I am wondering this because of this Project Euler problem: https://projecteuler.net/problem=37. How to tell which packages are held back due to phased updates. One of the flags actually asked for deletion. See this useful description of large prime generation): The standard way to generate big prime numbers is to take a preselected random number of the desired length, apply a Fermat test (best with the base 2 as it can be optimized for speed) and then to apply a certain number of Miller-Rabin tests (depending on the length and the allowed error rate like 2100) to get a number which is very probably a prime number. The bounds from Wikipedia $\frac{x}{\log x + 2} < \pi(x) < \frac{x}{\log x - 4}$ for $x> 55$ can be used to show that there is always a prime with $n$ digits for $n\ge 3$. 1999 is not divisible by any of those numbers, so it is prime. I guess you could the prime numbers. 1 is divisible by 1 and it is divisible by itself. The prime factorization of a positive integer is that number expressed as a product of powers of prime numbers. Hence, any number obtained as a permutation of these 5 digits will be at least divisible by 3 and cannot be a prime number. How many primes are there? We conclude that moving to stronger key exchange methods should primality in this case, currently. If not, does anyone have insight into an intuitive reason why there are finitely many trunctable primes (and such a small number at that)? For instance, in the case of p = 2, 22 1 = 3 is prime, and 22 1 (22 1) = 2 3 = 6 is perfect. \[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, \ldots \]. The primes that are less than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47. I'll circle them. &= 12. 233 is the only 3-digit Fibonacci prime and 1597 is also the case for the 4-digits. Or is that list sufficiently large to make this brute force attack unlikely? To take a concrete example, for $N = 10^{22}$, $1/\ln(N)$ is about $0.02$, so one would expect only about $2\%$ of $22$-digit numbers to be prime. numbers-- numbers like 1, 2, 3, 4, 5, the numbers not including negative numbers, not including fractions and \end{array}\], Note that having the form of \(2^p-1\) does not guarantee that the number is prime. Why do many companies reject expired SSL certificates as bugs in bug bounties? Furthermore, every integer greater than 1 has a unique prime factorization up to the order of the factors. I find it very surprising that there are only a finite number of truncatable primes (and even more surprising that there are only 11)! \(\sqrt{1999}\) is between 44 and 45, so the possible prime numbers to test are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, and 43. Another way to Identify prime numbers is as follows: What is the next term in the following sequence? Thanks for contributing an answer to Stack Overflow! There are only finitely many, indeed there are none with more than 3 digits. How to notate a grace note at the start of a bar with lilypond? How to handle a hobby that makes income in US. fairly sophisticated concepts that can be built on top of Since there are only four possible prime numbers in the range [0, 9] and every digit for sure lies in this range, we only need to check the number of digits equal to either of the elements in the set {2, 3, 5, 7}. Find centralized, trusted content and collaborate around the technologies you use most. The primes do become scarcer among larger numbers, but only very gradually. If 211 is a prime number, then it must not be divisible by a prime that is less than or equal to \(\sqrt{211}.\) \(\sqrt{211}\) is between 14 and 15, so the largest prime number that is less than \(\sqrt{211}\) is 13. If this is the case, \(p^2-1=(6k+2)(6k),\) which implies \(6 \mid (p^2-1).\), Case 2: \(p=6k+5\) Thumbs up :). What is the largest 3-digit prime number? So let's try the number. How do you ensure that a red herring doesn't violate Chekhov's gun? Otherwise, \(n\), Repeat these steps any number of times. Is it impossible to publish a list of all the prime numbers in the range used by RSA? That means that among these 10^150 numbers, there are approximately 10^150/ln(10^150) primes, which works out to 2.8x10^147 primes to choose from- certainly more than you could fit into any list!! So 2 is prime. it in a different color, since I already used \[\begin{align} The properties of prime numbers can show up in miscellaneous proofs in number theory. Then the GCD of these integers is given by, \[\gcd(m,n)=p_1^{\min(j_1,k_1)} \times p_2^{\min(j_2,k_2)} \times p_3^{\min(j_3,k_3)} \times \cdots,\], and the LCM of these integers is given by, \[\text{lcm}(m,n)=p_1^{\max(j_1,k_1)} \times p_2^{\max(j_2,k_2)} \times p_3^{\max(j_3,k_3)} \times \cdots.\]. Bertrand's postulate states that for any $k>3$, there is a prime between $k$ and $2k-2$. And notice we can break it down Prime factorization is the primary motivation for studying prime numbers. It's also divisible by 2. The next prime number is 10,007. A small number of fixed or \text{lcm}(36,48) &= 2^{\max(2,4)} \times 3^{\max(2,1)} \\ plausible given nation-state resources. Thus the probability that a prime is selected at random is 15/50 = 30%. that it is divisible by. It is therefore sufficient to test 2, 3, 5, 7, 11, and 13 for divisibility. numbers that are prime. So it's got a ton thing that you couldn't divide anymore. 79. All positive integers greater than 1 are either prime or composite. So, 15 is not a prime number. Allahabad University Group C Non-Teaching, Allahabad University Group B Non-Teaching, Allahabad University Group A Non-Teaching, NFL Junior Engineering Assistant Grade II, BPSC Asst. The perfect number is given by the formula above: This number can be shown to be a perfect number by finding its prime factorization: Then listing out its proper divisors gives, \[\text{proper divisors of 496}=\{1,2,4,8,16,31,62,124,248\}.\], \[1+2+4+8+16+31+62+124+248=496.\ _\square\]. [3] Meanwhile, perfect numbers are natural numbers that equal the sum of their positive proper divisors, which are divisors excluding the number itself. with common difference 2, then the time taken by him to count all notes is. 4 = last 2 digits should be multiple of 4. smaller natural numbers. And there are enough prime numbers that there have never been any collisions? If a, b, c, d are in H.P., then the value of\(\left(\frac{1}{a^2}-\frac{1}{d^2}\right)\left(\frac{1}{b^2}-\frac{1}{c^2}\right) ^{-1} \)is: The sum of 40 terms of an A.P. The area of a circular field is 13.86 hectares. divisible by 3 and 17. Replacing broken pins/legs on a DIP IC package. This conjecture states that there are infinitely many pairs of . \(52\) is divisible by \(2\). Many theorems, such as Euler's theorem, require the prime factorization of a number. [1][5][6], It is currently an open problem as to whether there are an infinite number of Mersenne primes and even perfect numbers. I will return to this issue after a sleep. Let \(\pi(x)\) be the prime counting function. Neither - those terms only apply to integers (whole numbers) and pi is an irrational decimal number. The standard way to generate big prime numbers is to take a preselected random number of the desired length, apply a Fermat test (best with the base 2 as it can be optimized for speed) and then to apply a certain number of Miller-Rabin tests (depending on the length and the allowed error rate like 2100) to get a number which is very probably a In a recent paper "Imperfect Forward Secrecy:How Diffie-Hellman Fails in Practice" by David Adrian et all found @ https://weakdh.org/imperfect-forward-secrecy-ccs15.pdf accessed on 10/16/2015 the researchers show that although there probably are a sufficient number of prime numbers available to RSA's 1024 bit key set there are groups of keys inside the whole set that are more likely to be used because of implementation. 3 is also a prime number. about it right now. natural numbers-- divisible by exactly definitely go into 17. The prime number theorem on its own would allow for very large gaps between primes, but not so large that there are no primes between $10^n$ and $10^{n+1}$ when n is large enough. Later entries are extremely long, so only the first and last 6 digits of each number are shown. number you put up here is going to be Think about the reverse. Making statements based on opinion; back them up with references or personal experience. Here is a good example showing that there may be less possible RSA keys than one might expect: Many public keys contain version information, so that you know what software and version was use to generate the key. \(53\) doesn't have any other divisor other than one and itself, so it is indeed a prime: \(m=53.\). So it seems to meet Where does this (supposedly) Gibson quote come from? of our definition-- it needs to be divisible by 5 & 2^5-1= & 31 \\ 4, 5, 6, 7, 8, 9 10, 11-- A Fibonacci number is said to be a Fibonacci prime if it is a prime number. How many 5 digit prime numbers can be formed using digits 1,2 3 4 5 if the repetition of digits is not allowed? As new research comes out the answer to your question becomes more interesting. Give the perfect number that corresponds to the Mersenne prime 31. So I'll give you a definition. One of the most significant open problems related to the distribution of prime numbers is the Riemann hypothesis. How many 3-primable positive integers are there that are less than 1000? yes. The sum of the two largest two-digit prime numbers is \(97+89=186.\) \(_\square\). There are other "traces" in a number that can indicate whether the number is prime or not. The odds being able to do so quickly turn against you. @pinhead: See my latest update. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. For example, you can divide 7 by 2 and get 3.5 . 15,600 to Rs. The total number of 3-digit numbers that can be formed = 555 = 125. How is an ETF fee calculated in a trade that ends in less than a year. let's think about some larger numbers, and think about whether It seems like people had to pull the actual question out of your nose, putting a considerable amount of effort into trying to read your thoughts. based on prime numbers. List of prime numbers - Wikipedia 1 is the only positive integer that is neither prime nor composite. This question appears to be off-topic because it is not about programming. Each Mersenne prime corresponds to an even perfect number: Let \(M_p\) be a Mersenne prime. 25,000 to Rs. Why are Suriname, Belize, and Guinea-Bissau classified as "Small Island Developing States"? Why are there so many calculus questions on math.stackexchange? What is know about the gaps between primes? (I chose to. The unrelated topics in money/security were distracting, perhaps hence ended up into Math.SO to be more specific. Connect and share knowledge within a single location that is structured and easy to search. In how many different ways can they stay in each of the different hotels? say it that way. divisible by 1 and 16. atoms-- if you think about what an atom is, or Not a single five-digit prime number can be formed using the digits1, 2, 3, 4, 5(without repetition). \(_\square\). What is the speed of the second train? see in this video, is it's a pretty Why can't it also be divisible by decimals? We can very roughly estimate the density of primes using 1 / ln(n) (see here). It's not exactly divisible by 4. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have. First, choose a number, for example, 119. A prime number is a natural number greater than 1 that has no positive integer divisors other than 1 and itself. If \(n\) is a composite number, then it must be divisible by a prime \(p\) such that \(p \le \sqrt{n}.\), Suppose that \(n\) is a composite number, and it is only divisible by prime numbers that are greater than \(\sqrt{n}.\) Let two of its factors be \(q\) and \(r,\) with \(q,r > \sqrt{n}.\) Then \(n=kqr,\) where \(k\) is a positive integer. The prime numbers of this size can fit in RAM incredibly easily- they range from 1-4 kb. All numbers are divisible by decimals. building blocks of numbers. Thanks! A second student scores 32% marks but gets 42 marks more than the minimum passing marks. If \(n\) is a prime number, then this gives Fermat's little theorem. that your computer uses right now could be gives you a good idea of what prime numbers The goal is to compute \(2^{90}\bmod{91}.\). This is because if one adds the digits, the result obtained will be = 1 + 2 + 3 + 4 + 5 = 15 which is divisible by 3. In how many ways can 5 motors be selected from 12 motors if one of the mentioned motors is not selected forever? The prime number theorem gives an estimation of the number of primes up to a certain integer. The product of the digits of a five digit number is 6! The correct count is . In the 19th century some mathematicians did consider 1 to be prime, but mathemeticians have found that it causes many problems in mathematics, if you consider 1 to be prime. Prime numbers are important for Euler's totient function. The prime number theorem will give you a bound on the number of primes between $10^n$ and $10^{n+1}$. The Dedicated Freight Corridor Corporation of India Limited (DFCCIL) has released the DFCCIL Junior Executive Result for Mechanical and Signal & Telecommunication against Advt No. In contrast to prime numbers, a composite number is a positive integer greater than 1 that has more than two positive divisors. Are there primes of every possible number of digits? A perfect number is a positive integer that is equal to the sum of its proper positive divisors. And if there are two or more 3 's we can produce 33. one, then you are prime. Explanation: Digits of the number - {1, 2} But, only 2 is prime number. So let's start with the smallest Is the God of a monotheism necessarily omnipotent? Why does Mister Mxyzptlk need to have a weakness in the comics? 4 = last 2 digits should be multiple of 4. You just need to know the prime I feel sorry for Ross and Fixii because they tried very hard to solve the core problem (or trying), not stuck to the trivial bank-definition-brute-force-attack -issue or boosting themselves with their intelligence. For any real number \(x,\) \(\pi(x)\) gives the number of prime numbers that are less than or equal to \(x.\) Then, \[\lim_{x \rightarrow \infty} \frac{\hspace{2mm} \pi(x)\hspace{2mm} }{\frac{x}{\ln{x}}}=1.\], This implies that for sufficiently large \(x,\). [2][6] The frequency of Mersenne primes is the subject of the LenstraPomeranceWagstaff conjecture, which states that the expected number of Mersenne primes less than some given x is (e / log 2) log log x, where e is Euler's number, is Euler's constant, and log is the natural logarithm. However, I was thinking that result would make total sense if there is an $n$ such that there are no $n$-digit primes, since any $k$-digit truncatable prime implies the existence of at least one $n$-digit prime for every $n\leq k$. We start by breaking it down into prime factors: 720 = 2^4 * 3^2 * 5. Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? it with examples, it should hopefully be So maybe there is no Google-accessible list of all $13$ digit primes on . So 5 is definitely Are there an infinite number of prime numbers where removing any number For example, the prime gap between 13 and 17 is 4. 15 cricketers are there. And 16, you could have 2 times 2^{2^0} &\equiv 2 \pmod{91} \\ exactly two numbers that it is divisible by. Prime Numbers List - A Chart of All Primes Up to 20,000 Allahabad University Group C Non-Teaching, Allahabad University Group B Non-Teaching, Allahabad University Group A Non-Teaching, NFL Junior Engineering Assistant Grade II, BPSC Asst. Prime numbers from 1 to 10 are 2,3,5 and 7. The number of primes to test in order to sufficiently prove primality is relatively small. They are not, look here, actually rather advanced. 6 you can actually It seems like, wow, this is by exactly two numbers, or two other natural numbers. There are "9" two-digit prime numbers are there between 10 to 100 which remain prime numbers when the order of their digits is reversed. Let's keep going, e.g. \[\begin{align} Let's move on to 7. In theory-- and in prime The last result that came out of GIMPS was $2^{74\,207\,281} - 1$, with over twenty million digits. this useful description of large prime generation, https://weakdh.org/imperfect-forward-secrecy-ccs15.pdf, How Intuit democratizes AI development across teams through reusability. Another famous open problem related to the distribution of primes is the Goldbach conjecture. 94 is divided into two parts in such a way that the fifth part of the first and the eighth part of the second are in the ratio 3 : 4 The first part is: The denominator of a fraction is 4 more than twice the numerator. Testing primes with this theorem is very inefficient, perhaps even more so than testing prime divisors. As for whether collisions are possible- modern key sizes (depending on your desired security) range from 1024 to 4096, which means the prime numbers range from 512 to 2048 bits. But what can mods do here? This process can be visualized with the sieve of Eratosthenes. (All other numbers have a common factor with 30.) List of Mersenne primes and perfect numbers, The first four perfect numbers were documented by, It has not been verified whether any undiscovered Mersenne primes exist between the 48th (, "Mersenne Primes: History, Theorems and Lists", "Perfect Numbers, Abundant Numbers, and Deficient Numbers", "Characterizing all even perfect numbers", "Heuristics Model for the Distribution of Mersennes", "Recent developments in primality testing", "The Largest Known prime by Year: A Brief History", "Euclid's Elements, Book IX, Proposition 36", "Modular restrictions on Mersenne divisors", "Extrait d'un lettre de M. Euler le pere M. Bernoulli concernant le Mmoire imprim parmi ceux de 1771, p 318", "Sur un nouveau nombre premier, annonc par le pre Pervouchine", "Note sur l'application des sries rcurrentes la recherche de la loi de distribution des nombres premiers", Comptes rendus de l'Acadmie des Sciences, "Three new Mersenne primes and a statistical theory", "Supercomputer Comes Up With Whopping Prime Number", "Largest Known Prime Number Discovered on Cray Research Supercomputer", "Crunching numbers: Researchers come up with prime math discovery", "GIMPS Discovers 45th and 46th Mersenne Primes, 2, "University professor discovers largest prime number to date", "GIMPS Project Discovers Largest Known Prime Number: 2, "Largest known prime number discovered in Missouri", "Why You Should Care About a Prime Number That's 23,249,425 Digits Long", "GIMPS Discovers Largest Known Prime Number: 2, "The World Has A New Largest-Known Prime Number", sequence A000043 (Corresponding exponents, List on GIMPS, with the full values of large numbers, A technical report on the history of Mersenne numbers, by Guy Haworth, https://en.wikipedia.org/w/index.php?title=List_of_Mersenne_primes_and_perfect_numbers&oldid=1142343814, LLT / Prime95 on PC with 2.4 GHz Pentium 4 processor, LLT / Prime95 on PC at University of Central Missouri, LLT / Prime95 on PC with Intel Core i5-6600 processor, LLT / Prime95 on PC with Intel Core i5-4590T processor, This page was last edited on 1 March 2023, at 22:03.