three consecutive odd numbers which are prime?
954148
3, 5, 7\n\nIn mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. There exists an infinitude of prime numbers, as demonstrated by Euclid in about 300 B.C.. 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 (sequence A000040 in OEIS); see the list of prime numbers for a longer list.\n\nThe property of being a prime is called primality, and the word prime is also used as an adjective. Since 2 is the only even prime number, the term odd prime refers to all prime numbers greater than 2.\n\nThe study of prime numbers is part of number theory, the branch of mathematics which encompasses the study of natural numbers. Prime numbers have been the subject of intense research, yet some fundamental questions, such as the Riemann hypothesis and the Goldbach conjecture, have been unresolved for more than a century. The problem of modelling the distribution of prime numbers is a popular subject of investigation for number theorists: when looking at individual numbers, the primes seem to be randomly distributed, but the "global" distribution of primes follows well-defined laws.\n\nThe notion of prime number has been generalized in many different branches of mathematics.
780131
1224=2*2*3*3*17\n4000=2*2*2*2*2*5*5*5\n6336=2*2*2*2*2*2*2*11\n3125=5*5*5*5*5\n\nNone. There is no prime # that is a factor of all; therefore, there is no #, prime/composite, that goes into all of them.
1172244
I don't know where this law of numbers came from....\n\nBut...\n\nMaybe what it should say is..."Any odd number with any given power can be expressed as a difference of one consecutive set of two perfect squares."...since that statement is true...\n\nThe difference between two consecutive squares is, in fact, the sequence of odd numbers.\n\nThis is interesting too, because all prime numbers will be included in this sequence, except for 2.
129925
- it's odd\n- it's prime\n- it's equal to the sum of the two prime numbers preceeding it ( = 2 + 3)\n- it's a Fermat prime (= 2^(2^1) + 1)\n- it's also a factorial prime (= 3! - 1)\n- it's successive to 4 \n- it preceeds 6\n- all its multiples end either by 5 or by 0\n- when dividing a whole number, it gives either another whole number or a finite decimal\n- each of its powers, when dividing a whole number, gives either another whole number or a finite decimal\n- the mean between 1 and its square root is equal to the golden ratio "Phi"\n\nwell, these are eleven, ten of which using only rationals
569147
The next three numbers are 108,138,150\nSubtract 1 from each numbers in the series, we get\n3,5,11,17,29,41,59,71,101,....which are prime numbers.\nAdd 1 to each numbers to get this series, 5,7,13,19,31,43,61,73,103,.....\nWe see that only those un-prime numbers are taken which are mean of two prime numbers.(for e.g 72 is the mean of 71 and 73). Un-prime number 24 is not taken because it is between 23 (prime) and 25 (un-prime).\nThe prime numbers after 103 are 107,109,113,127,131, 137,139,149,151,157,163,167,173,179,181,191 etc.\nFrom here we see 108, 138 and 150 are three numbers which are mean of two prime numbers.\n\nSo the next three numbers are 108,138,150\n\nGood question, thanks
324897
Could be 10,14,13. The odd terms differ by 3 (eg. 4-1,7-4), the even terms differ by 4.
1067732
If the N numbers:\n\np, p + d, p + 2d, ..., p + (N-1)d\n\nare all prime, and if q is a prime, then either:\n\nq divides d and all elements of the sequence have the same residue modulo q (which would be nonzero unless N=1 and p=q)\n\nor\n\nany q consecutive elements of the sequence make up a complete residue set modulo q, i.e., their remainders modulo q will be the set {0, 1, 2, ..., 1-1} not necessarily in that order.\n\nthen note that unless 3 divides d that the first three taken modulo 3 form a complete residue set (i.e., the remainders modulo 3 will be the set {0, 1, 2} in some order).  Likewise the first five taken modulo five will have remainders modulo five of {0, 1, 2, 3, 4} modulo five.  So searches for N consecutive primes in arithmetic progression usually take N to be a multiple of all of the primes less than or equal to N.\n\nA search for\n\nprime number records consecutive arithmetic progression\n\nin Google,\n\nhttp://www.google.com/search?q=prime+number+records+consecutive+arithmetic+progression\n\nyields as its first link\n\nPrime Arithmetic Progression -- from Wolfram MathWorld\nhttp://mathworld.wolfram.com/PrimeArithmeticProgression.html\n\nwhich contains some sample sequences (smaller p and larger N, smaller N and larger p) and says it was last updated Friday, May 12, 2006 -- sample quote from that page:\n\n"\nFor example, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089 is a 10-term arithmetic progression of primes with difference 210.\n"\n\n(note that 210 = 2 * 3 * 5 * 7 is the product of all primes less than or equal to ten).\n\nDan D
927457
Is there an infinite number of twin primes? (i.e. N and N+2 are both prime).\n\nFor other problems, see:\nhttp://mathworld.wolfram.com/UnsolvedProblems.html
1121426
I don't know if this is what you are looking for but simplified this fraction would be 24/43 (divided by 3). And you cannot simplify it any further because 43 is a prime number, as far as I remember...
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'.....)
320622
The question relates to two things:  the first is to determine basically what numbers it takes multiplied together to create the final number in question.\n\nTo do this, you start with the prime numbers, i.e., numbers which are only divisible by 1 and themselves.  Several examples of these would be 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, and so on.\n\nTake 352, for example:\n352/2 = 176\n176/2 = 88\n88/2 = 44\n44/2 = 22\n22/2 = 11\nYou have exhausted the number 2.  Now move on to the next prime number by which 11 is divisible.  As 11 itself IS a prime number, the answer is 11.\n\nThe second part of the question relates to exponential form.  How many times did you divide 352 by 2 until you hit an odd number?  Five times.  So, the exponential expression of the prime factorization of 352 is 2 to the 5 (which is not posible to illustrate here.  Write the number 2 and then write a small 5 to the upper right,) * 11\n\n2(5) * 11 = 352\n\nNow take the other two numbers.  If you look at the list I provided above, you will note that 89 is a prime number.\n\n1 * 89 = 89\n\nFinally, take 156.\n\n156/2 = 78\n78/2 = 39\n39/3 = 13\n\n2(2) * 3 * 13 = 156\n\nHope this helps.\n\nPlease take time to pick the best answer.\n\nI tip the hat to the people who chose to use the "^" key.  I could not think of a way to describe it otherwise.  Their representation is probably more valid than my use of parentheses, which would actually represent something else altogether.  Note well though that I indicated how to write "two to the fifth power" in my paragraph above.
467453
This can be proven by exhausing all the possibilities.  A prime number is defined as a number whose only factors are 1 and itself.  For the number 3, we need only check 1 number (the number 2), as 1 and 3 are already factors.  Dividing 2 into 3, we quickly find that the answer is 1.5, which shows that 2 is not a factor.  Therefore, the only factors of 3 are 1 and 3, which, according to the definition of a prime number, means that 3 is prime.
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
707944
1.132/3=43\nthe nos are 42,43 and 44\n\n2.76/2=38\nthe consecutive odd nos are 37 and 39\n\n3.x+3.04=6.24+1.2x\nadding -1.2x-6.24\n-0.2x-3.2=0\n-0.2x=3.2\ndividing by -0.2\nx=-16
948657
Without leaving anything out, find the greatest common factor of 45, 72, 63 and 36, which is 9.  So 9 care packages.\n\nRelatively prime means their GCF is 1.  The only multiples of 3 that are divisible by 6 are even ones, and if the first number were odd it would still be odd when you multiplied it by 3, so the first number must be even.  That means the second MUST be odd because if BOTH were even, they'd habe a common factor of 2.
899336
84, without even needing to check. That is 2*2*3*7, which gives 3 prime factors. You can't get 4, since 2*3*5*7 is too big.
1067663
Seven prime integers.\n\n7\n17\n37\n47\n67\n71\n73