So clearly, any number is 2^{2^2} &\equiv 16 \pmod{91} \\ and the other one is one. numbers-- numbers like 1, 2, 3, 4, 5, the numbers How many numbers in the following sequence are prime numbers? This conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. another color here. How do you get out of a corner when plotting yourself into a corner. How is an ETF fee calculated in a trade that ends in less than a year. I suppose somebody might waste some terabytes with lists of all of them, but they'll take a while to download.. EDIT: Google did not find a match for the $13$ digit prime 4257452468389. 71. However, this process can. 73. Thus, any prime \(p > 3\) can be represented in the form \(6k+5\) or \(6k+1\). is divisible by 6. So it is indeed a prime: \(n=47.\), We use the same process in looking for \(m\). In how many ways can 5 motors be selected from 12 motors if one of the mentioned motors is not selected forever? natural numbers-- 1, 2, and 4. [11] The discovery year and discoverer are of the Mersenne prime, since the perfect number immediately follows by the EuclidEuler theorem. That means that your prime numbers are on the order of 2^512: over 150 digits long. primality in this case, currently. But the, "which means the prime numbers range from 512 to 2048" - I think you mean 512 to 2048. divisible by 1 and 4. The product of the digits of a five digit number is 6! How far is the list of known primes known to be complete? Which of the following fraction can be written as a Non-terminating decimal? For more see Prime Number Lists. [2][4], There is a one-to-one correspondence between the Mersenne primes and the even perfect numbers. Why does a prime number have to be divisible by two natural numbers? This definition excludes the related palindromic primes. How many more words (not necessarily meaningful) can be formed using the letters of the word RYTHM taking all at a time? How is the time complexity of Sieve of Eratosthenes is n*log(log(n))? \[\begin{align} This number is also the largest known prime number. It's not divisible by 2. those larger numbers are prime. Is a PhD visitor considered as a visiting scholar? 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. Why are "large prime numbers" used in RSA/encryption? I suggested to remove the unrelated comments in the question and some mod did it. Identify those arcade games from a 1983 Brazilian music video. Union Public Service Commission (UPSC) has released the NDA I 2023Notification for 395 vacancies. \(_\square\). \(_\square\). All you can say is that Prime numbers from 1 to 10 are 2,3,5 and 7. Bertrand's postulate states that for any $k>3$, there is a prime between $k$ and $2k-2$. Let \(\pi(x)\) be the prime counting function. How many two-digit primes are there between 10 and 99 which are also prime when reversed? 3 & 2^3-1= & 7 \\ The rate of interest for which the same amount of interest can be received on the same sum after 5 years is. Weekly Problem 18 - 2016 . Not the answer you're looking for? atoms-- if you think about what an atom is, or This delves into complex analysis, in which there are graphs with four dimensions, where the fourth dimension is represented by the darkness of the color of the 3-D graph at its separate values. \(2^{11}-1=2047\) is not a prime number; its prime factorization is \(23 \times 89.\). I guess you could 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. "How many ten digit primes are there?" Prime Numbers in the range 100,000 to 200,000, Prime Numbers in the range 200,000 to 300,000, Prime Numbers in the range 300,000 to 400,000, Prime Numbers in the range 400,000 to 500,000, Prime Numbers in the range 500,000 to 600,000, Prime Numbers in the range 600,000 to 700,000, Prime Numbers in the range 700,000 to 800,000, Prime Numbers in the range 800,000 to 900,000, Prime Numbers in the range 900,000 to 1,000,000. I assembled this list for my own uses as a programmer, and wanted to share it with you. Or, is there some $n$ such that no primes of $n$-digits exist? A prime gap is the difference between two consecutive primes. 15,600 to Rs. \[\begin{align} 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. A chocolate box has 5 blue, 4 green, 2 yellow, 3 pink colored gems. 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. [Solved] How many 5-digit prime numbers can be formed using - Testbook Is the God of a monotheism necessarily omnipotent? irrational numbers and decimals and all the rest, just regular Redoing the align environment with a specific formatting. Prime and Composite Numbers Prime Numbers - Advanced Prime Number Lists. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have. divisible by 1 and itself. numbers that are prime. Yes, there is always such a prime. smaller natural numbers. We can arrange the number as we want so last digit rule we can check later. The simplest way to identify prime numbers is to use the process of elimination. 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. If you want an actual equation, the answer to your question is much more complex than the trouble is worth. give you some practice on that in future videos or Candidates who are qualified for the CBT round of the DFCCIL Junior Executive are eligible for the Document Verification & Medical Examination. So 1, although it might be 4, 5, 6, 7, 8, 9 10, 11-- That is a very, very bad sign. 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? Thanks! Sign up, Existing user? But it's also divisible by 7. The RSA method of encryption relies upon the factorization of a number into primes. Prime numbers are numbers that have only 2 factors: 1 and themselves. 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. &\vdots\\ 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. How many such numbers are there? A Fibonacci number is said to be a Fibonacci prime if it is a prime number. What is the harm in considering 1 a prime number? The LCM is given by taking the maximum power for each prime number: \[\begin{align} building blocks of numbers. 3 digit Prime Palindrome Numbers. - Mathematics Stack Exchange 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. Learn more about Stack Overflow the company, and our products. by anything in between. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. general idea here. Now \(p\) divides \(uab\) \((\)since it is given that \(p \mid ab),\) and \(p\) also divides \(vpb\). I am not sure whether this is desirable: many users have contributed answers that I do not wish to wipe out. 998 is the second largest 3-digit number, but as it is divisible by \(2\), it is not prime. divisible by 5, obviously. 999 is the largest 3-digit number, but as it is divisible by \(3\), it is not prime. Let's move on to 2. One of the most fundamental theorems about prime numbers is Euclid's lemma. And what you'll To crack (or create) a private key, one has to combine the right pair of prime numbers. 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. Approach: The idea is to iterate through all the digits of the number and check whether the digit is a prime or not. My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project. maybe some of our exercises. * instead. idea of cryptography. My program took only 17 seconds to generate the 10 files. How to match a specific column position till the end of line? 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. by exactly two natural numbers-- 1 and 5. \[\begin{align} But I'm now going to give you 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}. Direct link to Matthew Daly's post The Fundamental Theorem o, Posted 11 years ago. natural ones are who, Posted 9 years ago. So a number is prime if Kiran has 24 white beads and Resham has 18 black beads. for example if we take 98 then 9$\times$8=72, 72=7$\times$2=14, 14=1$\times$4=4. to talk a little bit about what it means 1234321&= 11111111\\ There are other methods that exist for testing the primality of a number without exhaustively testing prime divisors. \phi(2^4) &= 2^4-2^3=8 \\ 2 doesn't go into 17. Prime Numbers | Brilliant Math & Science Wiki agencys attacks on VPNs are consistent with having achieved such a Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? The primes do become scarcer among larger numbers, but only very gradually. And that includes the 3, so essentially the counting numbers starting divisible by 1 and 16. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. the answer-- it is not prime, because it is also By contrast, numbers with more than 2 factors are call composite numbers. The key theme is primality and, At money.stackexchange.com is the original expanded version of the question, which elaborated on the security & trust issues further. see in this video, or you'll hopefully Three travelers reach a city which has 4 hotels. with common difference 2, then the time taken by him to count all notes is. \(101\) has no factors other than 1 and itself. divisible by 1 and 3. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Therefore, \(\phi(10)=4.\ _\square\). It is divisible by 3. 3 = sum of digits should be divisible by 3. So instead of solving the key mathematical problem they wasted time on trivialities, the hidden mathematical problem stayed unsolved. What is the speed of the second train? It was unfortunate that the question went through many sites, becoming more confused, but it is in a way understandable because it is related to all of them. Finally, prime numbers have applications in essentially all areas of mathematics. The simple interest on a certain sum of money at the rate of 5 p.a. 5 Digit Prime Numbers List - PrimeNumbersList.com This means that each positive integer has a prime factorization that no other positive integer has, and the order of factors in a prime factorization does not matter. For example, 2, 3, 5, 13 and 89. And if you're \(_\square\). 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. Properties of Prime Numbers. These methods are called primality tests. How to deal with users padding their answers with custom signatures? But it's also divisible by 2. A 5 digit number using 1, 2, 3, 4 and 5 without repetition. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. In Math.SO, Ross Millikan found the right words for the problem: semi-primes. How many five-digit flippy numbers are divisible by . How do you get out of a corner when plotting yourself into a corner. Prime Number List - Math is Fun \(_\square\), We have \(\frac{12345}{5}=2469.\) So 12345 is divisible by 5 and therefore is not prime. But if we let 1 be prime we could write it as 6=1*2*3 or 6= 1*2 *1 *3. There are $308,457,624,821$ 13 digit primes and $26,639,628,671,867$ 15 digit primes. Therefore, this way we can find all the prime numbers. Palindromic number - Wikipedia (All other numbers have a common factor with 30.) \end{align}\]. Previous . Things like 6-- you could 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. 5 = last digit should be 0 or 5. Those are the two numbers How many numbers of 4 digits divisible by 5 can be formed with the digits 0, 2, 5, 6 and 9? Why do many companies reject expired SSL certificates as bugs in bug bounties? You can't break As new research comes out the answer to your question becomes more interesting. Two digit products into Primes - Mathematics Stack Exchange just so that we see if there's any rev2023.3.3.43278. So it's not two other Bulk update symbol size units from mm to map units in rule-based symbology. any other even number is also going to be How do we prove there are infinitely many primes? that your computer uses right now could be If this is the case, \(p^2-1=(6k+6)(6k+4),\) which implies \(6 \mid (p^2-1).\), One of the factors, \(p-1\) or \(p+1\), will be divisible by \(6\). 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. \end{array}\], Note that having the form of \(2^p-1\) does not guarantee that the number is prime. If a a three-digit number is composite, then it must be divisible by a prime number that is less than or equal to \(\sqrt{1000}.\) \(\sqrt{1000}\) is between 31 and 32, so it is sufficient to test all the prime numbers up to 31 for divisibility. 68,000, it is a golden opportunity for all job seekers. It seems like, wow, this is A train leaves Meerutat 5 a.m. and reaches Delhi at 9 a.m. Another train leaves Delhi at 7 a.m. and reaches Meerutat 10:30 a.m. At what time do the two trains cross each other? How to use Slater Type Orbitals as a basis functions in matrix method correctly? The sum of the two largest two-digit prime numbers is \(97+89=186.\) \(_\square\). Only the numeric values of 2,1,0,1 and 2 are used. That question mentioned security, trust, asked whether somebody could use the weakness to their benefit, and how to notify the bank of a problem . 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. 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. 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!! Let \(p\) be prime. Connect and share knowledge within a single location that is structured and easy to search. Numbers that have more than two factors are called composite numbers. Let's try out 5. Is it possible to create a concave light? Why is one not a prime number i don't understand? Fortunately, one does not need to test the divisibility of each smaller prime to conclude that a number is prime. Nearly all theorems in number theory involve prime numbers or can be traced back to prime numbers in some way. And now I'll give 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. If you have an $n$-digit prime, how many 'chances' do you have to extend it to an $(n+1)$-digit prime? \end{align}\]. That is, an emirpimes is a semiprime that is also a (distinct) semiprime upon reversing its digits. If you don't know What I try to do is take it step by step by eliminating those that are not primes. From 91 through 100, there is only one prime: 97. UPSC Civil Services Prelims 2023 Mock Test, CA 2022 - UPSC IAS & State PSC Current Affairs. Prime Number Lists - Math is Fun 2^{2^3} &\equiv 74 \pmod{91} \\ The most famous problem regarding prime gaps is the twin prime conjecture. In order to develop a prime factorization, one must be able to efficiently and accurately identify prime numbers. 79. Then \(\frac{M_p\big(M_p+1\big)}{2}\) is an even perfect number. Without loss of generality, if \(p\) does not divide \(b,\) then it must divide \(a.\) \( _\square \). Also, the result can be strengthened in the following sense (by the prime number theorem): For any $\epsilon > 0$, there is a $K$ such that for any $k > K$, there is a prime between $k$ and $(1+\epsilon)k$. acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Android App Development with Kotlin(Live), Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Find all the prime numbers of given number of digits, Solovay-Strassen method of Primality Test, Introduction to Primality Test and School Method, Write an iterative O(Log y) function for pow(x, y), Modular Exponentiation (Power in Modular Arithmetic), Euclidean algorithms (Basic and Extended), Program to Find GCD or HCF of Two Numbers, Finding LCM of more than two (or array) numbers without using GCD, Sieve of Eratosthenes in 0(n) time complexity. How to follow the signal when reading the schematic? Northern Coalfields Limited Fitter Mock Test, HAL Electronics - Management Trainees & Design Trainees Mock Test, FSSAI Technical Officer & Central Food Safety Officer Mock Test, DFCCIL Mechanical (Fitter) - Junior Executive Mock Test, IGCAR Mechanical - Technical Officer Mock Test, NMDC Maintenance Assistant Fitter Mock Test, IGCAR/NFC Electrician Stipendiary Trainee, BIS Mock Mock Test(Senior Secretariat Assistant & ASO), NIELIT (NIC) Technical Assistant Mock Test, Northern Coalfields Limited Previous Year Papers, FSSAI Technical Officer Previous Year Papers, AAI Junior Executive Previous Year Papers, DFCCIL Junior Executive Previous Year Papers, AAI JE Airport Operations Previous Year Papers, Vizag Steel Management Trainee Previous Year Papers, BHEL Engineer Trainee Previous Year Papers, NLC Graduate Executive Trainee Previous Year Papers, NPCIL Stipendiary Trainee Previous Year Papers, DFCCIL Junior Manager Previous Year Papers, NIC Technical Assistant A Previous Year Papers, HPCL Rajasthan Refinery Engineer Previous Year Papers, NFL Junior Engineering Assistant Grade II Previous Year Papers. \(_\square\), Let's work backward for \(n\). because one of the numbers is itself. Numbers that have more than two factors are called composite numbers. \hline I'll switch to 997 is not divisible by any prime number up to \(31,\) so it must be prime. What is 5 digit maximum prime number? And how did you find it - Quora for 8 years is Rs. Pleasant browsing for those who love mathematics at all levels; containing information on primes for students from kindergarten to graduate school. 97. You could divide them into it, &= 2^4 \times 3^2 \\ So 16 is not prime. There are other "traces" in a number that can indicate whether the number is prime or not. because it is the only even number This question is answered in the theorem below.) Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. are all about. Some people (not me) followed the link back to where it came from, and I would now agree that it is a confused question. How to notate a grace note at the start of a bar with lilypond? [1][5][6], It is currently an open problem as to whether there are an infinite number of Mersenne primes and even perfect numbers. A prime number is a whole number greater than 1 whose only factors are 1 and itself. Direct link to noe's post why is 1 not prime?, Posted 11 years ago. Prime factorizations are often referred to as unique up to the order of the factors. What can a lawyer do if the client wants him to be acquitted of everything despite serious evidence? What is know about the gaps between primes? Every integer greater than 1 is either prime (it has no divisors other than 1 and itself) or composite (it has more than two divisors). The question is still awfully phrased. \(_\square\). &= 12. \end{align}\]. 7 & 2^7-1= & 127 \\ How many semiprimes, etc? Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory.Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2 p 1 for some positive integer p.For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 1. The unrelated answers stole the attention from the important answers such as by Ross Millikan. And then maybe I'll The answer is that the largest known prime has over 17 million digits- far beyond even the very large numbers typically used in cryptography). of factors here above and beyond \[\begin{align} With a salary range between Rs. Discoverers denoted as "GIMPS / name" refer to GIMPS discoveries with hardware used by that person. So it seems to meet List out numbers, eliminate the numbers that have a prime divisor that is not the number itself, and the remaining numbers will be prime. Of how many primes it should consist of to be the most secure? After 2, 3, and 5, every prime leaves remainder 1, 7, 11, 13, 17, 19, 23, or 29 modulo 30. How many 3-primable positive integers are there that are less than 1000? Learn more in our Number Theory course, built by experts for you. 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 \(x,\). This, along with integer factorization, has no algorithm in polynomial time. Let us see some of the properties of prime numbers, to make it easier to find them. A factor is a whole number that can be divided evenly into another number. First, choose a number, for example, 119. For example, 5 is a prime number because it has no positive divisors other than 1 and 5. A train 100 metres long, moving at a speed of 50 km per hour, crosses another train 120 metres long coming from the opposite direction in 6 seconds. what encryption means, you don't have to worry UPSC NDA (I) Application Dates extended till 12th January 2023 till 6:00 pm. Common questions. based on prime numbers. 6!&=720\\ It is helpful to have a list of prime numbers handy in order to know which prime numbers should be tested. [Solved] How many five - digit prime numbers can be obtained - Testbook Otherwise, \(n\), Repeat these steps any number of times. For example, the prime gap between 13 and 17 is 4. But is the bound tight enough to prove that the number of such primes is a strictly growing function of $n$? The goal is to compute \(2^{90}\bmod{91}.\). I hope we can continue to investigate deeper the mathematical issue related to this topic. So, any combination of the number gives us sum of15 that will not be a prime number. Furthermore, all even perfect numbers have this form. implying it is the second largest two-digit prime number. Or is that list sufficiently large to make this brute force attack unlikely? what people thought atoms were when Any integer can be written in the form \(6k+n,\ n \in \{0,1,2,3,4,5\}\). Hence, any number obtained as a permutation of these 5 digits will be at least divisible by 3 and cannot be a prime number. Prime factorization is the primary motivation for studying prime numbers. Thus, there is a total of four factors: 1, 3, 5, and 15. Connect and share knowledge within a single location that is structured and easy to search. again, just as an example, these are like the numbers 1, 2, 2^{2^1} &\equiv 4 \pmod{91} \\ That question mentioned security, trust, asked whether somebody could use the weakness to their benefit, and how to notify the bank of a problem. And the definition might By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Thus the probability that a prime is selected at random is 15/50 = 30%. try a really hard one that tends to trip people up. whose first term is 2 and common difference 4, will be, The distance between the point P (2m, 3m, 4 m)and the x-axis is. How to handle a hobby that makes income in US. List of prime numbers - Wikipedia . Identify those arcade games from a 1983 Brazilian music video, Replacing broken pins/legs on a DIP IC package. So if you can find anything The fundamental theorem of arithmetic separates positive integers into two classifications: prime or composite. So I'll give you a definition. On the other hand, following the tracing back that Akhil did, I do not see why this question was even migrated here. Direct link to ajpat123's post Ate there any easy tricks, Posted 11 years ago. &= 2^2 \times 3^1 \\ How to Create a List of Primes Using the Sieve of Eratosthenes Is 51 prime? What are the values of A and B? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Can you write oxidation states with negative Roman numerals? definitely go into 17. A second student scores 32% marks but gets 42 marks more than the minimum passing marks. So let's try 16. divisible by 2, above and beyond 1 and itself. Ltd.: All rights reserved, that can be divided exactly only by itself(example - 2, 3, 5, 7, 11 etc.). \text{lcm}(36,48) &= 2^{\max(2,4)} \times 3^{\max(2,1)} \\ To subscribe to this RSS feed, copy and paste this URL into your RSS reader. 4 men board a bus which has 6 vacant seats. Euclid's lemma can seem innocuous, but it is incredibly important for many proofs in number theory. But as you progress through I closed as off-topic and suggested to the OP to post at security. natural number-- the number 1. It looks like they're . And I'll circle Why are there so many calculus questions on math.stackexchange? New user? It only takes a minute to sign up. If you think about it, could divide atoms and, actually, if And it's really not divisible a little counter intuitive is not prime. The term reversible prime may be used to mean the same as emirp, but may also, ambiguously, include the palindromic primes. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. 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. 5 & 2^5-1= & 31 \\ straightforward concept. it in a different color, since I already used Think about the reverse. In some sense, $2\%$ is small, but since there are $9\cdot 10^{21}$ numbers with $22$ digits, that means about $1.8\cdot 10^{20}$ of them are prime; not just three or four!
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