Distribution of Prime Numbers?
358011
let x=45.\n\n2x+1=91=7*13\n\n91 is not divisible by 3 or 5, nor is it a prime, nor a square of a prime.\n\nAny product of two distinct primes greater than 5 will be a counterexample to your claim.
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
436162
no it is not\nhere is a list\n\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, 101, 103, 107, 109, 113,\n127, 131, 137, 139, 149, 151, 157, 163, 167, 173,\n179, 181, 191, 193, 197, 199, 211, 223, 227, 229,\n233, 239, 241, 251, 257, 263, 269, 271, 277, 281,\n283, 293. \n\n\n\nhow did I find out?  google?  prime numbers between 100 and 200
1026561
Okay, your possible outcomes number 16. They are:\n\n1+1=2\n1+2=3\n1+3=4\n1+4=5\n2+1=3\n2+2=4\n2+3=5\n2+4=6\n3+1=4\n3+2=5\n3+3=6\n3+4=7\n4+1=5\n4+2=6\n4+3=7\n4+4=8\n\nYour probabilites are:\n2: 1/16\n3: 2/16\n4: 3/16\n5: 4/16\n6: 3/16\n7: 2/16\n8: 1/16\n\n2,3,5 and 7 are prime, thus the probability of rolling a prime is (1+2+4+2)/16 or 9/16 exactly.
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.
787272
There are no even odd numbers.  However, 2 is the only even prime number.  Is that what you meant?
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.
175248
Unfortunately I don't know of a quick method but I can help you a little here. \n\nFirst, as you probably already know, prime numbers can only be evenly divided by 1 and the number itself.\n\nSecond, since all numbers are a product of prime numbers you can save time in by not testing division by non-prime numbers like 4 and 6 and 9 and so on.\n\nThird, you only have to test those prime number that are smaller than the square root of the number.\n\nIn your example, 117, you need only test the prime numbers less than 10.81.... since that is the square root of 117. So do a trial divide of 117 by 2, 3, 5, and 7.\n\nOf course there are a few other rules that can help you eliminate the first three choices. If the number is odd, it can't be evenly divided by 2. If the sum of digits isn't divisible by 3 then the number isn't either. And all numbers that are divisible by 5 end in 5 or zero.\n\nFor 117, the number is odd so that eliminates 2. The sum of 1 and 1 and 7 is 9 which is divisible by 3 so 117 is divisible by three and therefore not prime.\n\nSo now you may notice that 117 is divisible by 3 and 39 but I said you only need to test numbers smaller than the square root. What about 39? Well, since the number is divisible by three that alone proves the number is not prime. If you want the full prime factorization, you need to keep dividing.\n\nGood luck.
662185
Irrational numbers don't have patterns, either.\n\nYou could take pi or e or sqrt(2) out to a hundered digits and stat test it.\n\nI just looked at sqrt(2), sqrt(3), and e.  I couldn't see any pattern to occurances.\n\nAlso, I can't think of any reason there would be more of some number than another.  For years, sqrt(prime) has been used as a source of random numbers.
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.
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.
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.
465400
2, 3, 5, 7, 11\n28\n\nFYI- 1 is not a prime number! It is only divisible by 1. To be a prime number, it must be divisible by 2 numbers.\n\nprime numbers up to 20-\n2, 3, 5, 7, 11, 13, 17, 19\n\nto find a prime number, start at the number 2. cross out every other number (that would be 4, 6, 8, even numbers). Then cross out every 3rd number, every 4th number, and so on. The remaining numbers are prime!\n\nHope this helps!
249626
A prime number is a natural number greater than 1 that can be divided evenly only by 1 and itself. The first few prime numbers are\n\n2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...
943730
This is Goldbach's conjecture and has NOT been proven\ntrue or false.  Good luck solving it!!\n\nI looked at the above answers, adn they dont seem to understand the question.  You shouldl have said:\n\nAny even number greater than 2 CAN be written as the sum of two primes. Prove true or false.
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.)
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.