Why are Prime numbers so useful for encryption and other security matters?
612262
A prime number is a positive integer greater than one that is divisible by no positive integers other than one and itself. A positive integer which is not prime and which is not equal to one is called a composite number. \n\nLook at page 3-4 of that pdf to get an idea.
899443
39 can be devided by 3 people.  Scary.  \n\nBut you get the jist of what is a prime and a square from the other posts.
136689
2*3*5*7*11*13 = 30030\n\nYou're correct.\n\n(I see questions regarding "1" as a prime - Google "prime numbers" and you'll find many links starting at 2. Just sayin'.....)
74381
Don't you think that maybe this so called "message board is not really for you" meaning you are not the target market of this "dumb" room...\n\nok the answer to your question is this\n\n\nfor (x=1; x<0; x = x++){\n println("the highest prime number is: " + x + " as of " + getdate());\n}\n\nthe largest prime number is x if this loop ever stop...
7923
There isn't one. Mathematicians are working on it, but they have yet to find a pattern that covers all prime numbers (except for the fact they are divisible only by themselves and one.) There are patterns that cover some prime numbers, such as paired primes (where the difference between the two prime numbers is 2, such as 5 and 7), but there is no currently known way to quickly produce or check primes, which has important implications for the RSA algorithm (used in PGP for example), which relies on the complexity of primes for its security.
1138566
Have a look at http://alumnus.caltech.edu/~chamness/prime.html - it's a Java prime number generator with source code
120534
No, prime numbers are numbers that cannot be divided by anything but itself and 1. 6, 12, 24, and 36 can all be divided by 2
701564
Prime numbers between through 1 to 100 is\n2 3 5 7 11 13 17 19 23 29 \n31 37 41 43 47 53 59 61 67 71 \n73 79 83 89 97....
22019
today we don't have practical to find all prime number. you can find a part of them through Mersenne number: 2^p-1 or Fermat number: 2^(2^n) with p is prime number and n is nature number
58522
Well, these guys do, and its not just for the 100 thousand dollar prize!! (The Electronic Frontier Foundation is offering a $100,000 award to the first person or group to discover a ten million digit prime number.)\n\n\n\n\nhttp://primes.utm.edu/lists/small/small3.html\n\nhttp://www.cmsu.edu/x85370.xml\n\nhttp://www.mersenne.org/prime.htm\n\n\n\nBtw, (2^30402457)-1 is the largest known prime number!!!
207196
There is an infinite number of primes.  They'll never be done.\n\nHow Many Primes are There? \n\nWe will now consider the question of how many prime numbers there are.  The following investigation of this question is over two thousand years old, and is attributed to Euclid. \n\nTwo possible answers to the question are that there are either finitely many primes, or there are infinitely many of them.  We will show that the first answer is not possible, and therefore there are infinitely many primes.  (This approach is referred to as "proof by contradiction."  In general, proof by contradiction works like this: we know that there are only two possible answers to a question; we assume that the first answer is the correct one, and then discover that this leads to an inconsistency; and so we conclude that it is actually the second of the two answers that is correct.) \n\nEuclid's Proof \n\nSo let's suppose that there are only finitely many primes, say n of them.  We could then make a list of these n primes, say p1, p2, ..., pn.  Then consider the integer \n\n\nobtained by multiplying all of the primes, and then adding 1.  This new number m is either prime or it is not.  If it is not, then it is divisible by some prime.  But we are supposing that the only primes are p1 through pn--and none of these primes divides m, for when m is divided by one of these primes, the remainder is 1.  This contradicts the known fact that every positive integer greater than 1 is divisible (evenly) by some prime.  So the conclusion must be that m is prime.  But clearly m is greater than all of the primes p1, p2, ..., pn , so this contradicts the supposition that p1, p2, ..., pn is a complete list of all primes.  Our conclusion is that there are not finitely many primes; there are infinitely many.
118857
Ahkens provided the correct answer and Aseem provided the correct answer and the formulaic method of determining the relevant prime numbers. If you are confused, an easier way of obtaining the prime numbers for low numbers like 255 is simply to start with the lowest primes and divide them into 255 until you exhaust the possibilities. Firstly, the definition of a prime number is a number that can be divided, without a remainder, only by itself and by 1. (The number 1 is itself, however, NOT considered to be a prime - notice that Aseem correctly excluded it from his answer despite it appearing in the results of his formulae). \n\nUsing this definition, the prime numbers between 0 and 100 are:\n\n2,3,5,7,11,13,17,19,23,29,\n31,37,41,43,47,53,59,61,\n67,71,73,79,83,89,97\n\nSo 2 is the first prime that fits the above definition; but 2 doesnt divide into 255 so it doesn't fit into this answer.\n\nNext is 3; 255 / 3 = 85 so 3 is your first number.\nNext prime is 5; 85 / 5 = 17 so 5 is your next number.\n17 is a prime because it too fits the definition so 17 is your next number and as there are no remainders you have solved the problem. 3,5,17
583419
yes..http://primes.utm.edu/curios/page.php/101.html
710401
A business would encode it's data when storing it on an electronic system for two primary reasons.  The first is to reduce storage space (compression) and the second is for security (encryption).
236680
A perfect square is the product of a whole number times itself, therefore, there is at least one whole number (its square root) which evenly factors into the number.  Since that is the case, the number can't be prime.\n\nOr you could argue the other way, a prime number is a number for which there is no other whole number (other than itself and 1) which can be a factor of it.  Since a perfect square has at least its square root as an factor, a prime cannot be a perfect square.
90213
it isn't prime: it's divisible by 7 (which is one of my favourite numbers).\nIf you add it to 668^2 you get 669^2 (but that's a trick you can do with every odd number).
1032500
Basically for security authentication etc. Most popular is X.509 used in digital certificates.