what is a prime number?
97999
In mathematics, a prime number (or a prime) is a natural number greater than one whose only positive divisors are one and itself. Said another way, a prime number can only be divided into equally by 1 and itself (3 is a prime number because 1 goes into it equally 3 times and 3 goes into it equally once, there is no remainder.) A natural number that is greater than one and is not a prime is called a composite number. The numbers zero and one are neither prime nor composite. The property of being a prime is called primality. Since 2 is the only even prime number, the term odd prime refers to all prime numbers greater than 2. Prime numbers are of course of prime importance in number theory.\n\nThe sequence of prime numbers begins as follows:\n\n2, 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, ... \n\n2 is the only even prime number
357003
if you take the number N and add one it must be prime... \n\ntake any number it can be writen as a product of primes, so in this case let us just examin N+1/p_j\n\nclearly N/p_j is an integer, and 1/p_j is clearly not an integer. \n\nSo if N were not prime then there would exist p_j such that N+1/p_j was an integer.   But that can not be true, therefore the assumption that there are only finitly many primes is incorrect, and the opposite is true, there are infinitly many primes QED
66697
(2^30402457)-1 is the largest known prime number!\n\n\nGIMPS found: 230402457-1, the 43rd known Mersenne!  Found December 15, 2005, announced on Christmas. \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\nhttp://primes.utm.edu/largest.html
499816
Factor each number into their prime factors.\nTake the greatest number of occurrences of each\nprime and use them and only them  as the factors of your answer.\n\n  For example 4 and 10. Primes for each are 2,2 and\n2,5. 2 occurs at most two times and 5 occurs at most\nonce. So the factors in your answer are 2,2,5\nand the answer is 20. \n  Concise but complete. Exhaustive but exclusive.\nThat's elegance.
594189
34,\n\nYou are having the series as 2 times <prime numbers>\n2*2, 2*3, 2*5, 2*7, 2*11, 2*13, 2*17, 2*19, 2*23...\n = \n4, 6, 10, 14, 22, 26, 34, 38, 46 ...
647768
Unless I have forgotten had to do prime factorization the answer is 2*61.  That is 122 can be divided by the prime number 2 leaving 61.  61 is also a prime number because it can only be divided by itself and 1.
65054
101 (b) is a prime number because it can't be divided (without leaving a remainder) by anything, except itself and 1.
941068
Its a bad question, but the answer they're probably looking for is 8.\n\nIts not prime numbers as some have suggested, because 1 isn't a prime number. (Prime numbers are  2,3,5,7,11 etc)\n\nIt looks like its supposed to be the Fibonacci series, but they've missed off the first 1\n\nThe Fibonacci series is    1, 1, 2, 3, 5, 8, 13, 21 etc
888908
The answer is 23475.\n\nLet's look at how I got there:\n\n\nThe first digit is a prime number:  2,3,5,7\n\nOne is not a prime, so anything starting with 1 is not actually an option.  There are two valid numbers, but one of them has repeating digits.\n\nGood.  That narrows it down a lot.\n\nThe third digit is twice the first digit:  Following from the numbers possible for the first digit, it's 4,6,10,or 14.  It obviously cannot be the last 2 since they are two digits.  That means it is either 4 or 6, and the first digit is 2 or 3.\n\nSo far we have\n2x4xx or\n3x6xx\n\nThe fourth digit is the third digit plus 3.  That's easy.  We now have\n2x47x or\n3x69x\n\nThe fifth digit is the difference between the first digit and the fourth digit.  7-2=5 and  9-3=6  We now have\n\n2x475 or\n3x696\n\nWait!  The second number has a repeated digit, 6.  It thus cannot be the number.\n\nLet's go on with option 1.  The second digit is the fifth digit minus the first digit.  5-2=3\n\nThe number is 23475.\n\n\nHope this helps.
865396
Prime factorization is basically simplifying a number into its prime factors.  A numerical example would help.\n\nHere's how you would simplify 100 into a prime factorization:\n\n100 = \n4*25 (these aren't prime numbers yet, thus factor again)\n2*2*5*5\n\nSince 2 and 5 are prime numbers, this is the prime factorization.  \n\n----------\n\nHope this helps
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.
1061835
Th next number is 18. It is going up by the first prime number, down by the second prime number, up by the third prime number, down by the fourth, up by the fifth, and down by the sixth. So the last number is up by the seventh prime number.
857498
In math, it means "can be divided" by numbers other than themselves (3 is divisible but only by 1 and itself). Prime numbers like 1, 3, 5, 7, 11, 13, 17, etc. are unique in that you can't divide them by another number to end up with another whole number. Non-prime numbers, like 4, 6, 8, 9, 10, 12, 14 and 16 are divisible because you can divide them by other numbers like 2, 3 or 4 and end up with another whole number (no decimals). Surely, some mathematician will explain this better and in more correct terms, but I did what I could on such short notice.
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
1114299
http://www.newscientist.com/article.ns?id=dn4438\n\nhttp://www.math.utah.edu/~alfeld/math/largeprime.html\n\nI just did a search on yahoo\n"largest prime number"\nKeep it in quotes.  You'll find a lot of info.\n\nThere are more recent sites like this one.\nhttp://en.wikipedia.org/wiki/Prime_number#Location_of_the_largest_known_prime
1137046
There is no highest prime number.  Euclid showed that given any supposed prime number, you can always construct a new prime number higher than it.  Therefore there cannot be a highest prime number.\n\nYou do it this way.  Suppose the highest prime number is supposed to be "m".  Take "m" and all the prime numbers lower than "m", multiply them all together, and add one.  This new number cannot be divided evenly by "m", because it has a remainder of 1.  It cannot be divided by the next lower prime, because that too gives a remainder of 1, and so on.  Thus, the assumption that there was a largest prime number must be incorrect.\n\nExample, say we think the largest prime is 5.  Multiply 5 * 3 * 2 and add one to get 31.  31 is prime.  QED.
619489
What is the first perfect number?\n(A perfect number is a number which is the sum of all its proper divisors/factors. e.g. 28=1+2+4+7+14)