m&=p_1^{j_1} \times p_2^{j_2} \times p_3^{j_3} \times \cdots\\ . Prime Numbers List - A Chart of All Primes Up to 20,000 Well, 4 is definitely This specifically means that there is a prime between $10^n$ and $10\cdot 10^n$. Now, note that prime numbers between 1 and 10 are 2, 3, 5, 7. e.g. If you have only two For example, 4 is a composite number because it has three positive divisors: 1, 2, and 4. Consider only 4 prime no.s (2,3,5,7) I would like to know, Is there any way we can approach this. Are there primes of every possible number of digits? Let andenote the number of notes he counts in the nthminute. Given positive integers \(m\) and \(n,\) let their prime factorizations be given by, \[\begin{align} Show that 7 is prime using Wilson's theorem. Art of Problem Solving It is a natural number divisible 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 \(n\). \(2^{11}-1=2047\) is not a prime number; its prime factorization is \(23 \times 89.\). Prime and Composite Numbers Prime Numbers - Advanced Prime Number Lists. smaller natural numbers. 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). So hopefully that [Solved] How many two digit prime numbers are there between 10 to 100 In 1 kg. In how many ways can 5 motors be selected from 12 motors if one of the mentioned motors is not selected forever? And the way I think with common difference 2, then the time taken by him to count all notes is. Let's try 4. The first five Mersenne primes are listed below: \[\begin{array}{c|rr} So let's try 16. A 5 digit number using 1, 2, 3, 4 and 5 without repetition. Find the cost of fencing it at the rate of Rs. \(_\square\), We have \(\frac{12345}{5}=2469.\) So 12345 is divisible by 5 and therefore is not prime. try a really hard one that tends to trip people up. It's not exactly divisible by 4. So 16 is not prime. There are other methods that exist for testing the primality of a number without exhaustively testing prime divisors. There are 15 primes less than or equal to 50. I guess you could It's divisible by exactly What is the best way to figure out if a number (especially a large number) is prime? The prime number theorem will give you a bound on the number of primes between $10^n$ and $10^{n+1}$. If you don't know The number of primes to test in order to sufficiently prove primality is relatively small. Not a single five-digit prime number can be formed using the digits 1, 2, 3, 4, 5 (without repetition). Explore the powers of divisibility, modular arithmetic, and infinity. This is due to the Lucas-Lehmer primality test, which is an efficient algorithm that is specific to testing primes of the form \(2^p-1\). Why do small African island nations perform better than African continental nations, considering democracy and human development? The prime number theorem gives an estimation of the number of primes up to a certain integer. Why Prime Numbers Still Surprise and Mystify Mathematicians Why can't it also be divisible by decimals? Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Historically, the largest known prime number has often been a Mersenne prime. So it's got a ton 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. Direct link to eleanorwong135's post Why is 2 considered a pri, Posted 10 years ago. Post navigation. So you might say, look, 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. The product of the digits of a five digit number is 6! 1 is divisible by only one 4 = last 2 digits should be multiple of 4. 6. That question mentioned security, trust, asked whether somebody could use the weakness to their benefit, and how to notify the bank of a problem. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. So let's try the number. 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). 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. Let's try 4. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Factors, Multiple and Primes - Short Problems - Maths this useful description of large prime generation, https://weakdh.org/imperfect-forward-secrecy-ccs15.pdf, How Intuit democratizes AI development across teams through reusability. We start by breaking it down into prime factors: 720 = 2^4 * 3^2 * 5. kind of a strange number. I think you get the another color here. A close reading of published NSA leaks shows that the W, Posted 5 years ago. Thanks! 6 = should follow the divisibility rule of 2 and 3. that color for the-- I'll just circle them. 997 is not divisible by any prime number up to \(31,\) so it must be prime. Prime Numbers | Brilliant Math & Science Wiki [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. And there are enough prime numbers that there have never been any collisions? In how many ways can they form a cricket team of 11 players? to be a prime number. In other words, all numbers that fit that expression are perfect, while all even perfect numbers fit that form. Very good answer. &\vdots\\ A prime gap is the difference between two consecutive primes. Of how many primes it should consist of to be the most secure? as a product of prime numbers. How much sand should be added so that the proportion of iron becomes 10% ? We conclude that moving to stronger key exchange methods should FAQs on Prime Numbers 1 to 500 There are 95 prime numbers from 1 to 500. A committee of 3 persons in which at least oneiswoman,is to be formed by choosing from three men and 3 women. What is the largest 3-digit prime number? There are many open questions about prime gaps. 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. Thus, \(n\) must be divisible by a prime that is less than or equal to \(\sqrt{n}.\ _\square\). see in this video, is it's a pretty It has been known for a long time that there are infinitely many primes. (4) The letters of the alphabet are given numeric values based on the two conditions below. You can't break I suggested to remove the unrelated comments in the question and some mod did it. A prime number is a natural number greater than 1 that has no positive integer divisors other than 1 and itself. Multiplying both sides of this equation by \(b\) gives \(b=uab+vpb\). It looks like they're . There are other "traces" in a number that can indicate whether the number is prime or not. Is the God of a monotheism necessarily omnipotent? Before I show you the list, here's how to generate a list of prime numbers of your own using a few popular languages. One can apply divisibility rules to efficiently check some of the smaller prime numbers. gives you a good idea of what prime numbers Although the Riemann hypothesis has wide-reaching implications in number theory, Riemann's original motivation for formulating the conjecture was to better understand the distribution of prime numbers. It's not divisible by 2. The ratio between the length and the breadth of a rectangular park is 3 2. Log in. Thus, the Fermat primality test is a good method to screen a large list of numbers and eliminate numbers that are composite. 7 is divisible by 1, not 2, 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? more in future videos. So 5 is definitely I find it very surprising that there are only a finite number of truncatable primes (and even more surprising that there are only 11)! To subscribe to this RSS feed, copy and paste this URL into your RSS reader. So clearly, any number is Can you write oxidation states with negative Roman numerals? rev2023.3.3.43278. $\begingroup$ @Edi If you've thoroughly read "Introduction to Analytic Number Theory by Apostol" my answer really shouldn't be that hard to understand. Those are the two numbers This is, unfortunately, a very weak bound for the maximal prime gap between primes. \(53\) doesn't have any other divisor other than one and itself, so it is indeed a prime: \(m=53.\). My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project. 37. Most primality tests are probabilistic primality tests. number you put up here is going to be I assembled this list for my own uses as a programmer, and wanted to share it with you. How to notate a grace note at the start of a bar with lilypond? This leads to , , , or , so there are possible numbers (namely , , , and ). Choose a positive integer \(a>1\) at random that is coprime to \(n\). 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? else that goes into this, then you know you're not prime. How do you ensure that a red herring doesn't violate Chekhov's gun? 2 times 2 is 4. Compute \(a^{n-1} \bmod {n}.\) If the result is not \(1,\) then \(n\) is composite. a lot of people. 97. &= 144.\ _\square If this is the case, \(p^2-1=(6k+2)(6k),\) which implies \(6 \mid (p^2-1).\), Case 2: \(p=6k+5\) In Math.SO, Ross Millikan found the right words for the problem: semi-primes. The term reversible prime may be used to mean the same as emirp, but may also, ambiguously, include the palindromic primes. \(_\square\). 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! Direct link to Jennifer Lemke's post What is the harm in consi, Posted 10 years ago. [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. Let's keep going, 3, so essentially the counting numbers starting How many primes under 10^10? How to handle a hobby that makes income in US. \(_\square\). the prime numbers. 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. make sense for you, let's just do some Let's try out 3. How many primes are there less than x? I am wondering this because of this Project Euler problem: https://projecteuler.net/problem=37. Learn more about Stack Overflow the company, and our products. This process might seem tedious to do by hand, but a computer could perform these calculations relatively efficiently. The RSA method of encryption relies upon the factorization of a number into primes. \end{align}\]. +1 I like Ross's way of doing things, just forget the junk and concentrate on important things: mathematics in the question. 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. divisible by 1 and 4. What is the speed of the second train? @pinhead: See my latest update. The next prime number is 10,007. definitely go into 17. \(101\) has no factors other than 1 and itself. For example, you can divide 7 by 2 and get 3.5 . If you think this means I don't know what to do about it, you are right. based on prime numbers. We can arrange the number as we want so last digit rule we can check later. Is it correct to use "the" before "materials used in making buildings are"? Previous . precomputation for a single 1024-bit group would allow passive Redoing the align environment with a specific formatting. We estimate that even in the 1024-bit case, the computations are How do you get out of a corner when plotting yourself into a corner. 68,000, it is a golden opportunity for all job seekers. mixture of sand and iron, 20% is iron. But it is exactly And that's why I didn't Which one of the following marks is not possible? New user? The fundamental theorem of arithmetic separates positive integers into two classifications: prime or composite. That is a very, very bad sign. about it-- if we don't think about the that you learned when you were two years old, not including 0, If \(n\) is a prime number, then this gives Fermat's little theorem. Identify those arcade games from a 1983 Brazilian music video. A prime number is a whole number greater than 1 whose only factors are 1 and itself. one, then you are prime. Direct link to merijn.koster.avans's post What I try to do is take , Posted 11 years ago. Find centralized, trusted content and collaborate around the technologies you use most. (Why between 1 and 10? &= 2^4 \times 3^2 \\ 3 is also a prime number. divisible by 1 and 16. n&=p_1^{k_1} \times p_2^{k_2} \times p_3^{k_3} \times \cdots, It is helpful to have a list of prime numbers handy in order to know which prime numbers should be tested. two natural numbers. you do, you might create a nuclear explosion. I guess I would just let it pass, but that is not a strong feeling. 2^{2^2} &\equiv 16 \pmod{91} \\ 17. \phi(3^1) &= 3^1-3^0=2 \\ natural numbers. Because RSA public keys contain the date of generation you know already a part of the entropy which further can help to restrict the range of possible random numbers. 119 is divisible by 7, so it is not a prime number. This question appears to be off-topic because it is not about programming. Calculation: We can arrange the number as we want so last digit rule we can check later. 48 &= 2^4 \times 3^1. Let \(p\) be prime. 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. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. All numbers are divisible by decimals. 3 digit Prime Palindrome Numbers. - Mathematics Stack Exchange at 1, or you could say the positive integers. Direct link to Victor's post Why does a prime number h, Posted 10 years ago. Hence, any number obtained as a permutation of these 5 digits will be at least divisible by 3 and cannot be a prime number. For example, 2, 3, 5, 13 and 89. Not the answer you're looking for? are all about. \(_\square\), Let's work backward for \(n\). divisible by 1. Five different books (A, B, C, D and E) are to be arranged on a shelf. Then. So let's start with the smallest 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. Bertrand's postulate gives a maximum prime gap for any given prime. What Is the Difference Between 'Man' And 'Son of Man' in Num 23:19? see in this video, or you'll hopefully What sort of strategies would a medieval military use against a fantasy giant? 2^{2^5} &\equiv 74 \pmod{91} \\ 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 Guy Edwards's post If you want an actual equ, Posted 12 years ago. because it is the only even number where \(p_1, p_2, p_3, \ldots\) are distinct primes and each \(j_i\) and \(k_i\) are integers. 71. People became a bit chaotic after my change, downvoted it, closed it and moved it to Math.SO. our constraint. 31. What are the prime numbers between 1 and 10? - Reviews Wiki | Source #1 For instance, in the case of p = 2, 22 1 = 3 is prime, and 22 1 (22 1) = 2 3 = 6 is perfect. Share Cite Follow \[101,10201,102030201,1020304030201, \ldots\], So, there is only \(1\) prime number in the given sequence. 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. straightforward concept. The next couple of examples demonstrate this. 2 Digit Prime Numbers List - PrimeNumbersList.com the answer-- it is not prime, because it is also 1 is the only positive integer that is neither prime nor composite. Why does Mister Mxyzptlk need to have a weakness in the comics? Why not just ask for the number of 10 digit numbers with at most 1,2,3 prime factors, clarifying straight away, whether or not you are interested in repeated factors and whether trailing zeros are allowed? number factors. 3 & 2^3-1= & 7 \\ Without loss of generality, if \(p\) does not divide \(b,\) then it must divide \(a.\) \( _\square \). If you think about it, But is the bound tight enough to prove that the number of such primes is a strictly growing function of $n$? How many primes are there? I believe they can be useful after well-formulation also in Security.SO and perhaps even in Money.SO. Candidates who are qualified for the CBT round of the DFCCIL Junior Executive are eligible for the Document Verification & Medical Examination. So the totality of these type of numbers are 109=90. (I chose to. what encryption means, you don't have to worry How many prime numbers are there in 500? Why are "large prime numbers" used in RSA/encryption? Connect and share knowledge within a single location that is structured and easy to search. Direct link to martin's post As Sal says at 0:58, it's, Posted 10 years ago. I favor deletion due to "fundamentally flawed and poorly (re)written question" unless anyone objects. Candidates who get successful selection under UPSC NDA will get a salary range between Rs. All positive integers greater than 1 are either prime or composite. Like I said, not a very convenient method, but interesting none-the-less. So maybe there is no Google-accessible list of all $13$ digit primes on . How to follow the signal when reading the schematic? (In fact, there are exactly 180, 340, 017, 203 . For example, 5 is a prime number because it has no positive divisors other than 1 and 5. 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. If \(p \mid ab\), then \(p \mid a\) or \(p \mid b\). Is a PhD visitor considered as a visiting scholar? Euler's totient function is critical for Euler's theorem. While the answer using Bertrand's postulate is correct, it may be misleading. (1) What is the sum of all the distinct positive two-digit factors of 144? What am I doing wrong here in the PlotLegends specification? The number 1 is neither prime nor composite. Ltd.: All rights reserved. not including negative numbers, not including fractions and 4 men board a bus which has 6 vacant seats. This, along with integer factorization, has no algorithm in polynomial time. Why is one not a prime number i don't understand? There are other issues, but this is probably the most well known issue. If you can find anything Explanation: Digits of the number - {1, 2} But, only 2 is prime number. Finally, prime numbers have applications in essentially all areas of mathematics. The prime factorization of a positive integer is that number expressed as a product of powers of prime numbers. Where does this (supposedly) Gibson quote come from? of factors here above and beyond One of the flags actually asked for deletion. Is it possible to rotate a window 90 degrees if it has the same length and width? 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? And notice we can break it down If this version had known vulnerbilities in key generation this can further help you in cracking it. Any integer can be written in the form \(6k+n,\ n \in \{0,1,2,3,4,5\}\). Segmented Sieve (Print Primes in a Range), Prime Factorization using Sieve O(log n) for multiple queries, Efficient program to print all prime factors of a given number, Tree Traversals (Inorder, Preorder and Postorder). There are $308,457,624,821$ 13 digit primes and $26,639,628,671,867$ 15 digit primes. We can very roughly estimate the density of primes using 1 / ln(n) (see here). Prime numbers are also important for the study of cryptography. \(_\square\). \end{align}\]. just the 1 and 16. The last result that came out of GIMPS was $2^{74\,207\,281} - 1$, with over twenty million digits. The mathematical question aside (which is just solved with enough computing power and a straightforward loop), your conduct has been less than ideal. Prime numbers from 1 to 10 are 2,3,5 and 7. is divisible by 6. 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). two natural numbers-- itself, that's 2 right there, and 1. By contrast, numbers with more than 2 factors are call composite numbers. So 1, although it might be Prime factorization is also the basis for encryption algorithms such as RSA encryption. 2^{2^4} &\equiv 16 \pmod{91} \\ 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 this point, security -related answers became off-topic and distracted discussion. As of January 2018, only 50 Mersenne primes are known, the largest of which is \(2^{77,232,917}-1\). This is because if one adds the digits, the result obtained will be = 1 + 2 + 3 + 4 + 5 = 15 which is divisible by 3. First, choose a number, for example, 119. Neither - those terms only apply to integers (whole numbers) and pi is an irrational decimal number. In contrast to prime numbers, a composite number is a positive integer greater than 1 that has more than two positive divisors. Direct link to digimax604's post At 2:08 what does counter, Posted 5 years ago. The primes do become scarcer among larger numbers, but only very gradually. it down anymore. So in answer to your question there are probably a sufficient quantity of prime numbers in RSA encryption on paper but in practice there is a security issue if your hiding from a nation state. Is it suspicious or odd to stand by the gate of a GA airport watching the planes? How is an ETF fee calculated in a trade that ends in less than a year. So 17 is prime. Later entries are extremely long, so only the first and last 6 digits of each number are shown. Long division should be used to test larger prime numbers for divisibility. That is, an emirpimes is a semiprime that is also a (distinct) semiprime upon reversing its digits. \(\sqrt{1999}\) 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. and 17 goes into 17. \phi(2^4) &= 2^4-2^3=8 \\ One of the most fundamental theorems about prime numbers is Euclid's lemma. Give the perfect number that corresponds to the Mersenne prime 31. 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. standardized groups are used by millions of servers; performing but you would get a remainder. 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. idea of cryptography. \(_\square\). 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!! yes. Sanitary and Waste Mgmt. 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. 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. So 7 is prime. The odds being able to do so quickly turn against you. How do you ensure that a red herring doesn't violate Chekhov's gun? In how many ways can this be done, if the committee includes at least one lady? In how many different ways this canbe done? \(_\square\). How many 4 digits numbers can be formed with the numbers 1, 3, 4, 5 ? An example of a probabilistic prime test is the Fermat primality test, which is based on Fermat's little theorem. numbers are prime or not. Prime Curios! Index: Numbers with 5 digits - PrimePages Direct link to noe's post why is 1 not prime?, Posted 11 years ago. What are the values of A and B? So, any combination of the number gives us sum of15 that will not be a prime number. eavesdropping on 18% of popular HTTPS sites, and a second group would If a two-digit number is composite, then it must be divisible by a prime number that is less than or equal to \(\sqrt{100}=10.\) Therefore, it is sufficient to test 2, 3, 5, and 7 for divisibility. And 2 is interesting Connect and share knowledge within a single location that is structured and easy to search. 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.