Which is the only even prime number?
830770
2 is the only even prime number, and it divides evenly into every even number. 2 is the smallest factorial prime and the only factorial that is prime.  The first 30 prime numbers are 2, 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, and 113 .\n\nPrime numbers are numbers greater than 1 that are divisible by exactly two numbers: 1 and themselves. For example, the prime numbers through 20 are 2, 3, 5, 7, 11, 13, 17 and 19. As numbers grow larger, prime numbers become scarcer. If you examine the numbers from 1 to 100, you'll find that 25% of them are prime numbers. When you extend the list and check the numbers from 1 to 1000, the percentage drops dramatically to 16.8%. Only about 7% of the numbers from 1 to 1,000,000 are prime numbers.\n\nMathematicians believe (but have not conclusively proven) that every even number is the sum of two prime numbers except for the number 2.♥
28467
I just had a math packet dealing with this topic.  There are many equations out there that deal with finding primes, but all so far fail at a certain point in the sequence.  The method you refer to, called the Sieve of Eratosthenes, was developed by its namesake in Greece sometime between the 500s and 350 B.C. and is so far the only proven method to find primes.  Sorry, but unfortunately, there is no other accurate choice.
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.
1045069
There are currently 43 known Mersenne Primes (of the form 2^p-1, where p is prime).  All numbers up to the 39th prime have been exhaustively searched (see the mersenne.org status page) but there are gaps beyond that so it is possible that there is/are more Mersenne Primes between some of the later numbers.  I've denoted those with ? in the sequence numbering.  \n\nThe numbers get pretty large, so after awhile all I can give you is the number in the form 2^p-1 and the number of digits in the number.  You can go look up the long form if you really need it. :) \n\n1) 2^2-1 = 3\n2) 2^3-1 = 7\n3) 2^5-1 = 31\n4) 2^7-1 = 127\n5) 2^13-1 = 8191\n6) 2^17-1 = 131071\n7) 2^19-1 = 524287\n8) 2^31-1 = 2147483647\n9) 2^61-1 = 2 305 843 009 213 693 951\n10) 2^89-1 = 618 970 019 642 690 137 449 562 111\n11) 2^107-1 = 162 259 276 829 213 363 391 578 010 288 127\n12) 2^127-1 = 170 141 183 460 469 231 731 687 303 715 884 105 727\n13) 2^521-1 = 157 digits\n14) 2^607-1 = 183 digits\n15) 2^1,279-1 = 386 digits\n16) 2^2,203-1 = 664 digits\n17) 2^2,281-1 = 687 digits\n18) 2^3,217-1 = 969 digits\n19) 2^4,253-1 = 1,281 digits\n20) 2^4,423-1 = 1,332 digits\n21) 2^9,689-1 = 2,917 digits\n22) 2^9,941-1 = 2,993 digits\n23) 2^11,213-1 = 3,376 digits\n24) 2^19,937-1 = 6,002 digits\n25) 2^21,701-1 = 6,533 digits\n26) 2^23,209-1 = 6,987 digits\n27) 2^44,497-1 = 13,395 digits\n28) 2^86,243-1 = 25,962 digits\n29) 2^110,503-1 = 33,265 digits\n30) 2^132,049-1 = 39,751 digits\n31) 2^216,091-1 = 65,050 digits\n32) 2^756,839-1 = 227,832 digits\n33) 2^859,433-1 = 258,716 digits\n34) 2^1,257,787-1 = 378,632 digits\n35) 2^1,398,269-1 = 420,921 digits\n36) 2^2,976,221-1 = 895,932 digits\n37) 2^3,021,377-1 = 909,526 digits\n38) 2^6,972,593-1 = 2,098,960 digits\n39) 2^13,466,917-1 = 4,053,946 digits\n40?) 2^20,996,011-1 = 6,320,430 digits\n41?) 2^24,036,583-1 = 7,235,733 digits\n42?) 2^25,964,951-1 = 7,816,230 digits\n43?) 2^30,402,457-1 = 9,152,052 digits\n\nAnd if you want to know the English name of that 43rd known Mersenne prime, it starts, "three hundred fifteen tremillia millia quin quagin millia sescendo octo gintillion, four hundred sixteen tremillia millia quin quagin millia sescenun octo gintillion..."  (See the last link for the full name.)
787272
There are no even odd numbers.  However, 2 is the only even prime number.  Is that what you meant?
417502
In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:\n\nEvery even integer greater than 2 can be written as the sum of two primes. (The same prime may be used twice.) \nFor example,\n\n  4 = 2 + 2 \n  6 = 3 + 3 \n  8 = 3 + 5 \n10 = 3 + 7 = 5 + 5 \n12 = 5 + 7 \n14 = 3 + 11 = 7 + 7 \netc. \n\nHope that helps
982295
A prime number is a positive integer such that the only integers which evenly divide it are 1 and itself.\n\nFor example, 7 is prime because only 1 and 7 divide it evenly.\n\nThe sequence of prime numbers begins thus:\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 ...\nAnd there are infinitely many of them.\n\nhttp://en.wikipedia.org/wiki/Prime_number
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.
129045
Even numbers are divisible by 2 (2,4,6,8,10, etc) whereas odd are not (1,3,5,7,9, etc)
22351
Many have tried, yet none have found a formula. As noted on MathWorld,\n\n"Euler commented "Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate" (Havil 2003, p. 163). In a 1975 lecture, D. Zagier commented "There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision" (Havil 2003, p. 171)."
14699
Yes.\n\nFor any finite set of primes, there will always exist another prime not in that set.  So there can never be a "complete" finite set of all prime numbers.\n\nTake all known primes:\nP1, P2, P3,... Pn\nwhere Pn is the greatest prime.\n\n(P1 x P2 x P3 x.... x Pn) + 1 is not divisible by any of the known primes.\n\nIf it is not prime, then its prime factors are not in the original known set of primes.\n\nIf it is prime, then it itself is a prime that is not in the original known set of primes.
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
643237
2 is the only (and hence also the highest) even prime number.\n\nOther even numbers would be divisible by 2 besides itself and 1, so they cannot be prime.
545916
4, 9, 25, 49\nPerfect squares such that the square root is a prime number.
263111
I don't particularly have a favorite number, but I have some interesting observations from other's numbers.\n\nOut of 44 whole numbers provided so far, 29 of them are prime numbers. \n\nA full 66% of all numbers were prime. Interesting, because there are only 12.6% prime numbers between 1 and 7919. I would suggest that there is a significantly high proportion of primes to non-primes.\n\nThe highest prime as a favorite was 347. I wonder if this was a deliberate choice, or a subconcious preference. \n\nI could hypothesize that people are naturally drawn towards primes because they seem 'unique' and 'different' - Everyone wants to stand out. \n\nAnyway, Interesting. I wonder if anyone has ever done a study that would relate primes to people's unique number choices.
317639
the largest known prime number till date is (2^30402457)-1\n\nFor detailed reference visit:\n\nhttp://primes.utm.edu/largest.html\n\nand\n\nhttp://primes.utm.edu/lists/top_ten/topten.pdf
1046257
Conjectured, but not proven.\nhttp://en.wikipedia.org/wiki/Lenstra-Pomerance-Wagstaff_conjecture\n\n"Are there infinitely many Mersenne primes?"\nhttp://primes.utm.edu/mersenne/index.html\n\n"Equivalently we could ask: Are there infinitely many even perfect numbers?  The answer is probably yes (because the harmonic series diverges)."