How many primes do we know about?
361110
The one millionth prime is 15,485,863.  Check out the site below.
331994
In reply to Just wondering, yes they have, the biggest prime that has been found (in December 2005) has over 9 million digits (it's 9,152,052 digits long). \n\nThis is the latest (no 43) in the list of Mersenne Primes, which are all of the form (2^n) -1 where n is prime. (But not all values of n generate a Mersenne prime, only a tiny minority.)\n\nThat took a supercomputer 50 days to find. This was part of GIMPS, the Great Internet Mersenne Prime Search. The previous record, a featherweight weighing in at a mere 7 million digits, in Feb 2005 was also found by a GIMPS team member. \n\nWhen a number with more than ten million digits is found, there is a prize of 100,000 dollars to be claimed by the lucky winner, so you can see what drives them!  \n\nMerin Mersenne was a French monk who first investigated this problem some 350 years ago, Though Euclid was on the case back in 300 BC in Egypt.\n\nAnd it is to the list of Mersenne primes that we need to turn to answer the question.\n\nThe 14th and 15th Mersenne Primes would seem to meet the requirements of the question. Both were discovered in 1952 by someone called Robinson.\n\nM14  (2^607) -1  183 digits  \nM15  (2^1279) -1  386 sigits\n\nThe first two Mersenne primes that are themselves longer than 400 digits are M16 and M17, also discovered by Robinson\n\nM16  (2^ 2203) - 1  664 digits  \nM17  (2^ 2281) - 1  687  digits
522039
Primes from 50 to 100\n53\n59\n61\n67\n71\n73\n79\n83\n89\n97
216982
2, 3, 5, 7, 11, 13, 17, 19\n1 is NOT prime
630729
2.Only even number to be prime
994057
1 is not considered prime or composite partly because it was not considered a number far back in time, according to my first source.\n\nMy second source goes into great detail saying that one is not a prime number because mathematician do not want to break already existing patterns.
653675
Yes.  If you assume there are a finite number prime numbers, then a list of them would look like a1, a2, ..., an.  If you can make this number...\n\n(a1)(a2)(a3)...(an) + 1\n\n...then dividing this number by any of the known primes, you would have a remainder of 1, so therefore this number is a prime.  This is a contradiction that the primes are finite, so the primes must be infinite.
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
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.
1019600
Because every counting number is either a prime or is made up of them (except 1).  Maybe not the T.O.E., but they explain alot about how numbers relate to each other.
738875
To see what conjecture they are interested in, it really is necessary to consider a number of examples, exactly as they said. So lets set up a table. We will call the product in question N.\nRemember that we are only interested in prime numbers for p.\n\np               N                N/p\n---------------------------------\n2                    2               1\n3                    3               1\n5                  25               5\n7                721           103\n11      3628801     329891\n13  479001601 36846277\n\nNotice that the numbers N so far have all been divisible by p. So, if we represented  them on a p-clock, they would all be p o'clock (or 0 o'clock if you prefer). That is the conjecture they are interested in. You are supposed to conjecture that the value of 1*2*3*...*(p-1)+1 in p-hour arithmetic is always p o'clock.
147038
prime numbers sound special \n2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
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).
482620
All primes (ignoring 2) are odd.\n\nDivide odd numbers into 3 groups: those of the form 6n - 1, those of the form 6n + 1, and those of the form 6n + 3.\n\nIgnoring 3 itself, all primes are of the form 6n + 1 or 6n - 1, as all numbers of the form 6n + 3 or 6n - 3 are divisible by 3 and not prime. \n\nYour proposition follows from that fact.
777706
You make the assumption that there are a finite number of primes.\nIf this is so, then it is possible to write them all out in a list.\nYou then multiply them all together, and add one to the product.\nThe result is not divisible by any of your existing prime numbers. So it is either the case that:\nIt is not divisible by any number, i.e. it is prime.\nIt is divisible by two or more prime numbers, which cannot be on your list.\nEither way, you have missed out at least one prime number. Therefore, not matter what your list of prime numbers, you have always missed out some, which means that there is an infinite number of primes.
807869
the prime factorization can be figured out by repeatedly dividing the number by a prime number.\n for example 12\n 12 divided by 2 = 6,   6 divided by 2= 3,  3 divided by 3= 1\n the answer is 1.\ni hope this was helpful.
850647
Too long to print but here's the website\n\n(2^3021376)(2^3021377-1)\n\nThere are 1,819,050 digits\n\nhttp://www.calendarhome.com/prime/perfect4.html\n\nPlease note that the highest perfect prime number currently known, will continue to change when a higher one is found.