6 you can actually The sequence of emirps begins 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, (sequence A006567 in the OEIS). I find it very surprising that there are only a finite number of truncatable primes (and even more surprising that there are only 11)! \(51\) is divisible by \(3\). The probability that a prime is selected from 1 to 50 can be found in a similar way. m) is: Assam Rifles Technical and Tradesmen Mock Test, Physics for Defence Examinations Mock Test, DRDO CEPTAM Admin & Allied 2022 Mock Test, Indian Airforce Agniveer Previous Year Papers, Computer Organization And Architecture MCQ. So maybe there is no Google-accessible list of all $13$ digit primes on . \(_\square\). Some people (not me) followed the link back to where it came from, and I would now agree that it is a confused question. What is the sum of the two largest two-digit prime numbers? {10^1000, 10^1001}]" generates a random 1000 digit prime in 0.40625 seconds on my five year old desktop machine. Choose a positive integer \(a>1\) at random that is coprime to \(n\). 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. Which of the following fraction can be written as a Non-terminating decimal? Not the answer you're looking for? fairly sophisticated concepts that can be built on top of Since it only guarantees one prime between $N$ and $2N$, you might expect only three or four primes with a particular number of digits. If you don't know \(52\) is divisible by \(2\). Below is the implementation of this approach: Time Complexity: O(log10N), where N is the length of the number.Auxiliary Space: O(1), Count numbers in a given range having prime and non-prime digits at prime and non-prime positions respectively, Count all prime numbers in a given range whose sum of digits is also prime, Count N-digits numbers made up of even and prime digits at odd and even positions respectively, Maximize difference between sum of prime and non-prime array elements by left shifting of digits minimum number of times, Java Program to Maximize difference between sum of prime and non-prime array elements by left shifting of digits minimum number of times, Cpp14 Program to Maximize difference between sum of prime and non-prime array elements by left shifting of digits minimum number of times, Count numbers in a given range whose count of prime factors is a Prime Number, Count primes less than number formed by replacing digits of Array sum with prime count till the digit, Count of prime digits of a Number which divides the number, Sum of prime numbers without odd prime digits. Direct link to eleanorwong135's post Why is 2 considered a pri, Posted 10 years ago. Well actually, let me do 37. I'll circle the 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. Compute \(a^{n-1} \bmod {n}.\) If the result is not \(1,\) then \(n\) is composite. This definition excludes the related palindromic primes. haven't broken it down much. you do, you might create a nuclear explosion. However, this process can. straightforward concept. So 2 is prime. Direct link to ajpat123's post Ate there any easy tricks, Posted 11 years ago. It's divisible by exactly Posted 12 years ago. The term reversible prime may be used to mean the same as emirp, but may also, ambiguously, include the palindromic primes. Solution 1. . What is the harm in considering 1 a prime number? There are other methods that exist for testing the primality of a number without exhaustively testing prime divisors. So there is always the search for the next "biggest known prime number". Nearly all theorems in number theory involve prime numbers or can be traced back to prime numbers in some way. pretty straightforward. What about 17? But it's also divisible by 2. 7 & 2^7-1= & 127 \\ When it came to math.stackexchage it was a set of questions of simple mathematical fact, which could be answered without regard to the motivation. \text{lcm}(36,48) &= 2^{\max(2,4)} \times 3^{\max(2,1)} \\ Are there primes of every possible number of digits? 17. For example, 2, 3, 5, 13 and 89. Is it correct to use "the" before "materials used in making buildings are"? As of November 2009, the largest known emirp is 1010006+941992101104999+1, found by Jens Kruse Andersen in October 2007. This leads to , , , or , so there are possible numbers (namely , , , and ). 1 is divisible by 1 and it is divisible by itself. Prime numbers act as "building blocks" of numbers, and as such, it is important to understand prime numbers to understand how numbers are related to each other. From 31 through 40, there are again only 2 primes: 31 and 37. If \(n\) is a prime number, then this gives Fermat's little theorem. Which one of the following marks is not possible? The properties of prime numbers can show up in miscellaneous proofs in number theory. Can you write oxidation states with negative Roman numerals? Main Article: Fundamental Theorem of Arithmetic. 6= 2* 3, (2 and 3 being prime). Discoverers denoted as "GIMPS / name" refer to GIMPS discoveries with hardware used by that person. 3 is also a prime number. Thus, there is a total of four factors: 1, 3, 5, and 15. We conclude that moving to stronger key exchange methods should How many numbers of 4 digits divisible by 5 can be formed with the digits 0, 2, 5, 6 and 9? In theory-- and in prime 2^{2^0} &\equiv 2 \pmod{91} \\ Sanitary and Waste Mgmt. Sign up to read all wikis and quizzes in math, science, and engineering topics. This question appears to be off-topic because it is not about programming. the idea of a prime number. For any integer \(n>3,\) there always exists at least one prime number \(p\) such that, This implies that for the \(k^\text{th}\) prime number, \(p_k,\) the next consecutive prime number is subject to. Direct link to Victor's post Why does a prime number h, Posted 10 years ago. How to notate a grace note at the start of a bar with lilypond? The research also shows a flaw in TLS that could allow a man-in-middle attacker to downgrade the encryption to 512 bit. 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. In how many different ways can the letters of the word POWERS be arranged? Counting backward, we have the following: If 1999 is composite, then it must be divisible by a prime number that is less than or equal to \(\sqrt{1999}\). Candidates who get successful selection under UPSC NDA will get a salary range between Rs. A factor is a whole number that can be divided evenly into another number. Find the cost of fencing it at the rate of Rs. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have. I left there notices and down-voted but it distracted more the discussion. An important result dignified with the name of the ``Prime Number Theorem'' says (roughly) that the probability of a random number of around the size of $N$ being prime is approximately $1/\ln(N)$. 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. We've kind of broken One can apply divisibility rules to efficiently check some of the smaller prime numbers. Is a PhD visitor considered as a visiting scholar? \[\begin{align} The numbers p corresponding to Mersenne primes must themselves . To subscribe to this RSS feed, copy and paste this URL into your RSS reader. But it is exactly try a really hard one that tends to trip people up. UPSC NDA (I) Application Dates extended till 12th January 2023 till 6:00 pm. This is the complete index for the prime curiosity collection--an exciting collection of curiosities, wonders and trivia related to prime numbers and integer factorization. 3 times 17 is 51. If you have only two My program took only 17 seconds to generate the 10 files. 720 &\equiv -1 \pmod{7}. But the, "which means the prime numbers range from 512 to 2048" - I think you mean 512 to 2048. That means that your prime numbers are on the order of 2^512: over 150 digits long. 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Is there a solution to add special characters from software and how to do it. So it seems to meet The goal is to compute \(2^{90}\bmod{91}.\). Thanks! [7][8][9] It is also not known if any odd perfect numbers exist; various conditions on possible odd perfect numbers have been proven, including a lower bound of 101500. eavesdropping on 18% of popular HTTPS sites, and a second group would 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). The area of a circular field is 13.86 hectares. Or, is there some $n$ such that no primes of $n$-digits exist? For example, his law predicts 72 primes between 1,000,000 and 1,001,000. The product of the digits of a five digit number is 6! How to tell which packages are held back due to phased updates. For instance, I might say that 24 = 3 x 2 x 2 x 2 and you might say 24 = 2 x 2 x 3 x 2, but we each came up with three 2's and one 3 and nobody else could do differently. So it is indeed a prime: \(n=47.\), We use the same process in looking for \(m\). For example, 5 is a prime number because it has no positive divisors other than 1 and 5. our constraint. It has been known for a long time that there are infinitely many primes. The next prime number is 10,007. For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. But, it was closed & deleted at OP's request. Prime factorization is also the basis for encryption algorithms such as RSA encryption. Officer, MP Vyapam Horticulture Development Officer, Patna Civil Court Reader Cum Deposition Writer, NDA (Held On: 18 Apr 2021) Maths Previous Year paper, Electric charges and coulomb's law (Basic), Copyright 2014-2022 Testbook Edu Solutions Pvt. Bertrand's postulate (an ill-chosen name) says there is always a prime strictly between $n$ and $2n$ for $n\gt 1$. How to match a specific column position till the end of line? New user? they first-- they thought it was kind of the When both the numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator. I will return to this issue after a sleep. Divide the chosen number 119 by each of these four numbers. I think you get the of them, if you're only divisible by yourself and Bulk update symbol size units from mm to map units in rule-based symbology. To commemorate $50$ upvotes, here are some additional details: Bertrand's postulate has been proven, so what I've written here is not just conjecture. The number of different orders in which books A, B and E may be arranged is, A school committee consists of 2 teachers and 4 students. \(2^{11}-1=2047\) is not a prime number; its prime factorization is \(23 \times 89.\). standardized groups are used by millions of servers; performing In how many different ways this canbe done? divisible by 1 and itself. And if you're Of those numbers, list the subset of numbers that are co-prime to 10: This set contains 4 elements. Actually I shouldn't [3] Meanwhile, perfect numbers are natural numbers that equal the sum of their positive proper divisors, which are divisors excluding the number itself. Is there a formula for the nth Prime? So one of the digits in each number has to be 5. I don't know whether it was due to math-phobia or due to something else but many important mathematically-oriented security-biased questions came to Math.SO (they should belong to Security.SO), a rabbit-rabbit problem at the best. They want to arrange the beads in such a way that each row contains an equal number of beads and each row must contain either only black beads or only white beads. it in a different color, since I already used The consequence of these two theorems is that the value of Euler's totient function can be computed efficiently for any positive integer, given that integer's prime factorization. $\begingroup$ @Edi If you've thoroughly read "Introduction to Analytic Number Theory by Apostol" my answer really shouldn't be that hard to understand. 4.40 per metre. Before I show you the list, here's how to generate a list of prime numbers of your own using a few popular languages. All numbers are divisible by decimals. The problem is that it assumes a perfect PRNG to generate this amount of unique numbers to derive the primes from. But it's also divisible by 7. In Math.SO, Ross Millikan found the right words for the problem: semi-primes. However, if \(q\) and \(r\) are both greater than \(\sqrt{n},\) then \(qr>n.\) This cannot be true, because \(n=kqr,\) and \(k\) is a positive integer. \(_\square\). Multiple Years Age 11 to 14 Short Challenge Level. A Fibonacci number is said to be a Fibonacci prime if it is a prime number. 1 is a prime number. And hopefully we can The most notable problem is The Fundamental Theorem of Arithmetic, which says any number greater than 1 has a unique prime factorization. Give the perfect number that corresponds to the Mersenne prime 31. It seems that the question has been through a few revisions on sister sites, which presumably explains why some of the answers have to do with things like passwords and bank security, neither of which is mentioned in the question. Let's move on to 7. Each number has the same primes, 2 and 3, in its prime factorization. &\equiv 64 \pmod{91}. divisible by 1 and 4. Well, 4 is definitely Direct link to Sonata's post All numbers are divisible, Posted 12 years ago. (In fact, there are exactly 180, 340, 017, 203 . . I'm confused. Ltd.: All rights reserved, that can be divided exactly only by itself(example - 2, 3, 5, 7, 11 etc.). 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!! numbers are pretty important. How to Create a List of Primes Using the Sieve of Eratosthenes \end{align}\]. Considering the answers it has already received it should've been closed as off-topic at security.SE and re-asked anew here. Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? So clearly, any number is I answered in that vein. So if you can find anything Identify those arcade games from a 1983 Brazilian music video, Replacing broken pins/legs on a DIP IC package. A prime number is a numberthat can be divided exactly only by itself(example - 2, 3, 5, 7, 11 etc.). If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. none of those numbers, nothing between 1 1 is divisible by only one natural number-- the number 1. \phi(3^1) &= 3^1-3^0=2 \\ So, it is a prime number. In other words, all numbers that fit that expression are perfect, while all even perfect numbers fit that form. For example, you can divide 7 by 2 and get 3.5 . If not, does anyone have insight into an intuitive reason why there are finitely many trunctable primes (and such a small number at that)? With a salary range between Rs. the second and fourth digit of the number) . It means that something is opposite of common-sense expectations but still true.Hope that helps! \(49\) is divisible by \(7\), and from the property of primes it is enough information to conclude that the number is not prime. I suggested to remove the unrelated comments in the question and some mod did it. So 17 is prime. 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. 2^{2^3} &\equiv 74 \pmod{91} \\ So 1, although it might be (All other numbers have a common factor with 30.) Is it possible to create a concave light? I hope mods will keep topics relevant to the key site-specific-discussion i.e. Like I said, not a very convenient method, but interesting none-the-less. I closed as off-topic and suggested to the OP to post at security. This wouldn't be true if we considered 1 to be a prime number, because then someone else could say 24 = 3 x 2 x 2 x 2 x 1 and someone else could say 24 = 3 x 2 x 2 x 2 x 1 x 1 x 1 x 1 and so on, Sure, we could declare that 1 is a prime and then write an exception into the Fundamental Theorem of Arithmetic, but all in all it's less hassle to just say that 1 is neither prime nor composite. On the one hand, I agree with Akhil that I feel bad about wiping out contributions from the users. Feb 22, 2011 at 5:31. Let's try out 3. There is no such combination of 1, 2, 3, 4 and 5 that will give us a prime number. But it's the same idea Testing primes with this theorem is very inefficient, perhaps even more so than testing prime divisors. allow decryption of traffic to 66% of IPsec VPNs and 26% of SSH Staging Ground Beta 1 Recap, and Reviewers needed for Beta 2, Generate big prime numbers for RSA encryption algorithm. :), Creative Commons Attribution/Non-Commercial/Share-Alike. Let \(\pi(x)\) be the prime counting function. There would be an infinite number of ways we could write it. I favor deletion due to "fundamentally flawed and poorly (re)written question" unless anyone objects. \(_\square\), Let's work backward for \(n\). You can't break How to deal with users padding their answers with custom signatures? Direct link to noe's post why is 1 not prime?, Posted 11 years ago. This reduces the number of modular reductions by 4/5. for 8 years is Rs. We start by breaking it down into prime factors: 720 = 2^4 * 3^2 * 5. And that's why I didn't 997 is not divisible by any prime number up to \(31,\) so it must be prime. them down anymore they're almost like the So let's try the number. And the definition might The LCM is given by taking the maximum power for each prime number: \[\begin{align} \[\begin{align} The simple interest on a certain sum of money at the rate of 5 p.a. natural numbers. one, then you are prime. Without loss of generality, if \(p\) does not divide \(b,\) then it must divide \(a.\) \( _\square \). I mean, they have to be "small" enough to fit in RAM or some kind of limit like that? Direct link to Fiona's post yes. It's not divisible by 2, so So yes- the number of primes in that range is staggeringly enormous, and collisions are effectively impossible. number factors. examples here, and let's figure out if some because it is the only even number \(\sqrt{1999}\) 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. In short, the number of $n$-digit numbers increases with $n$ much faster than the density of primes decreases, so the number of $n$-digit primes increases rapidly as $n$ increases. A prime number is a natural number greater than 1 that has no positive integer divisors other than 1 and itself. I need a few small primes (say 10 to 300 digits) Mersenne Numbers What are the known Mersenne primes? \gcd(36,48) &= 2^{\min(2,4)} \times 3^{\min(2,1)} \\ Very good answer. It only takes a minute to sign up. The next couple of examples demonstrate this. divisible by 1 and 16. see in this video, or you'll hopefully 31. This should give you some indication as to why . The five digit number A679B, in base ten, is divisible by 72. 5 & 2^5-1= & 31 \\ The nature of simulating nature: A Q&A with IBM Quantum researcher Dr. Jamie We've added a "Necessary cookies only" option to the cookie consent popup. behind prime numbers. Direct link to Matthew Daly's post The Fundamental Theorem o, Posted 11 years ago. Am I mistaken in thinking that the security of RSA encryption, in general, is limited by the amount of known prime numbers? A committee of 3 persons in which at least oneiswoman,is to be formed by choosing from three men and 3 women. 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. Minimising the environmental effects of my dyson brain. The distribution of the values directly relate to the amount of primes that there are beneath the value "n" in the function. Now with that out of the way, In reality PRNG are often not as good as they should be, due to lack of entropy or due to buggy implementations. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. How can we prove that the supernatural or paranormal doesn't exist? Chris provided a good answer but with a misunderstanding about the word bank, I initially assumed that people would consider bank with proper security measures but they did not and the tone was lecturing-and-sarcastic. A prime gap is the difference between two consecutive primes. plausible given nation-state resources. be a priority for the Internet community. Let's try out 5. Only the numeric values of 2,1,0,1 and 2 are used. From 21 through 30, there are only 2 primes: 23 and 29. On the other hand, it is a limit, so it says nothing about small primes. Common questions. 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. Any number, any natural 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 Jeff's open design works perfect: people can freely see my view and Cris's view. There are only 3 one-digit and 2 two-digit Fibonacci primes. How many prime numbers are there (available for RSA encryption)? and the other one is one. One of the most fundamental theorems about prime numbers is Euclid's lemma. So you might say, look, We now know that you @willie the other option is to radically edit the question and some of the answers to clean it up. Ate there any easy tricks to find prime numbers? Using prime factorizations, what are the GCD and LCM of 36 and 48? The term palindromic is derived from palindrome, which refers to a word (such as rotor or racecar) whose spelling is unchanged when its letters are reversed. By using our site, you 6 = should follow the divisibility rule of 2 and 3. 73. 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). Thus the probability that a prime is selected at random is 15/50 = 30%. 2^{2^6} &\equiv 16 \pmod{91} \\ Replacing broken pins/legs on a DIP IC package. 2^{2^5} &\equiv 74 \pmod{91} \\ For example, the prime gap between 13 and 17 is 4. 1234321&= 11111111\\ 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. 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. counting positive numbers. If this version had known vulnerbilities in key generation this can further help you in cracking it. Direct link to SLow's post Why is one not a prime nu, Posted 2 years ago. \(_\square\). The GCD is given by taking the minimum power for each prime number: \[\begin{align} Why do many companies reject expired SSL certificates as bugs in bug bounties? Direct link to Peter Collingridge's post Neither - those terms onl, Posted 10 years ago. 8, you could have 4 times 4. if 51 is a prime number. Any 3 digit palindrome number is of type "aba" where b can be chosen from the numbers 0 to 9 and a can be chosen from 1 to 9. Calculation: We can arrange the number as we want so last digit rule we can check later. Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? and 17 goes into 17. The primes do become scarcer among larger numbers, but only very gradually. The sum of the two largest two-digit prime numbers is \(97+89=186.\) \(_\square\). And there are enough prime numbers that there have never been any collisions? Ifa1=a2= . =a10= 150anda10,a11 are in an A.P. What about 51? 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). what encryption means, you don't have to worry So it's got a ton FAQs on Prime Numbers 1 to 500 There are 95 prime numbers from 1 to 500. it down into its parts. 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 $n\ge 3$. That is, an emirpimes is a semiprime that is also a (distinct) semiprime upon reversing its digits. \(p^2-1\) can be factored to \((p+1)(p-1).\), Case 1: \(p=6k+1\) \(_\square\). Well, 3 is definitely that is prime. How many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number? yes. Words are framed from the letters of the word GANESHPURI as follows, then the true statement is. How do you get out of a corner when plotting yourself into a corner.
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