What is the largest known consecutive prime?
537907
This site has a table of primes p where 1 < p < 1,000,000,000,000\n\nIf you want to know N, you'll have to count them.
411704
Do you mean the 26th Mersenne Prime? It has already been found, In 1978.\n\nIt is (2^23209) - 1, a number with 6,987 digits in it.\n\nThey are up to 43 Mersenne Primes now. All Mersenne Primes are of the form (2^n) -1, where n is prime, but only a minority of prime values of n generate a Mersenne number.\n\nIt takes many days of looking by supercomputers to find these very large numbers, the largest of which has over 9 million digits. That took 50 days to find and 5 days to check that it had no factors. \n\nThere is no formula, just systematic trial and error and dividing by all primes up to the square root of the candidate prime to see if they divide into it (modulo 0) exactly or not.\n\nThe 26th ordinary prime, counting from 2 upwards as the 1st prime number, is relatively small in comparison.\n\n2, 3, 5, 7, 11\n13, 17, 19, 23, 29\n31, 37, 41, 43, 47\n53, 59, 61, 67, 71,\n73, 79, 83, 89, 97 \n\nmaking the 26th prime 101
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).
980553
The following is a link to a calculator which will generated large prime numbers as well as multiply huge numbers together:\nhttp://world.std.com/~reinhold/BigNumCalc.html\n\n716111958663682417342303150142 608858901789417310093684696588 037024637209566331209352948311 017575749961619319828641955426 693304570465688762892415366806 836017495077860594429200032782\n63334056542642264651\n\nX\n\n580216645856397911811840259504 402483982261360695169382324936 875058224718365368242988227337 103422506977399968259382326419 406708576245141031259861340509 976971601273015479957884681378\n87651823707102007839\n\n=\n\n415500078713497281558905442483 784251718409580288016708180261 624957845916174034681385215800 377996269949769240101176290536 233429600607265291665503850867 426580947888398820550079218757 303625094649132652959885439006 834654658500398125929731018350 466670499118257135230989594968 432239652495895326959857212205 024845334097138922197109779294 150585092298147887850145072541 456311267636214499699970863002\n4114599189\n\n********************* **************************\nYou can also use this site if you just want the prime numbers:\nhttp://primes.utm.edu/lists/small/small2.html#200\nYou would want to pick two that are 200 digits long and such that the product of the first two digits is 2 digits long.
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
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
293052
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97\n\n101 is the next prime number ... \nso 24 prime numbers between 1 - 100
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.
1014042
The range of consecutive prime numbers for a "strictly" 9-digit product begins at 463 (* 467 * 479 = 103569859) and ends with 991 (* 997 * 1009 = 996919243).  Within this numerical range, there are NO consecutive primes whose product results in unique digits.\n\nEven if you expand the definition of a 9-digit product to include those with a leading zero as a digit, you can also check all 8-digit products and consider the first digit to be a zero.  The range then begins at 211 (* 223 * 227 = 010681031).  Unfortunately, even with this expanded definition, there are no products with unique digits.  (The solution 233*239*241=13420567 is incorrect because if expressed as nine digits, the product becomes 013420567 which repeats the 0 digit.)\n\nFor the morbidly curious, the full solution set follows:\n\n211 x 223 x 227 = 10681031 -- 0x3 1x3 repeat\n223 x 227 x 229 = 11592209 -- 0x2 1x2 2x2 9x2 repeat\n227 x 229 x 233 = 12112039 -- 0x2 1x3 2x2 repeat\n229 x 233 x 239 = 12752323 -- 2x3 3x2 repeat\n233 x 239 x 241 = 13420567 -- 0x2 repeat\n239 x 241 x 251 = 14457349 -- 4x3 repeat\n241 x 251 x 257 = 15546187 -- 1x2 5x2 repeat\n251 x 257 x 263 = 16965341 -- 1x2 6x2 repeat\n257 x 263 x 269 = 18181979 -- 1x3 8x2 9x2 repeat\n263 x 269 x 271 = 19172437 -- 1x2 7x2 repeat\n269 x 271 x 277 = 20193023 -- 0x3 2x2 3x2 repeat\n271 x 277 x 281 = 21093827 -- 0x2 2x2 repeat\n277 x 281 x 283 = 22027871 -- 0x2 2x3 7x2 repeat\n281 x 283 x 293 = 23300239 -- 0x3 2x2 3x3 repeat\n283 x 293 x 307 = 25456133 -- 3x2 5x2 repeat\n293 x 307 x 311 = 27974761 -- 7x3 repeat\n307 x 311 x 313 = 29884301 -- 0x2 8x2 repeat\n311 x 313 x 317 = 30857731 -- 0x2 3x2 7x2 repeat\n313 x 317 x 331 = 32842151 -- 1x2 2x2 repeat\n317 x 331 x 337 = 35360399 -- 0x2 3x3 9x2 repeat\n331 x 337 x 347 = 38706809 -- 0x3 8x2 repeat\n337 x 347 x 349 = 40811711 -- 0x2 1x4 repeat\n347 x 349 x 353 = 42749359 -- 4x2 9x2 repeat\n349 x 353 x 359 = 44227723 -- 2x3 4x2 7x2 repeat\n353 x 359 x 367 = 46508809 -- 0x3 8x2 repeat\n359 x 367 x 373 = 49143869 -- 4x2 9x2 repeat\n367 x 373 x 379 = 51881689 -- 1x2 8x3 repeat\n373 x 379 x 383 = 54143561 -- 1x2 4x2 5x2 repeat\n379 x 383 x 389 = 56466073 -- 0x2 6x3 repeat\n383 x 389 x 397 = 59147839 -- 9x2 repeat\n389 x 397 x 401 = 61927633 -- 3x2 6x2 repeat\n397 x 401 x 409 = 65111573 -- 1x3 5x2 repeat\n401 x 409 x 419 = 68719771 -- 1x2 7x3 repeat\n409 x 419 x 421 = 72147191 -- 1x3 7x2 repeat\n419 x 421 x 431 = 76027969 -- 0x2 6x2 7x2 9x2 repeat\n421 x 431 x 433 = 78568283 -- 8x3 repeat\n431 x 433 x 439 = 81927497 -- 7x2 9x2 repeat\n433 x 439 x 443 = 84208541 -- 0x2 4x2 8x2 repeat\n439 x 443 x 449 = 87320173 -- 0x2 3x2 7x2 repeat\n443 x 449 x 457 = 90900499 -- 0x4 9x4 repeat\n449 x 457 x 461 = 94593973 -- 3x2 9x3 repeat\n457 x 461 x 463 = 97543451 -- 4x2 5x2 repeat\n461 x 463 x 467 = 99677881 -- 7x2 8x2 9x2 repeat\n463 x 467 x 479 = 103569859 -- 5x2 9x2 repeat\n467 x 479 x 487 = 108938491 -- 1x2 8x2 9x2 repeat\n479 x 487 x 491 = 114537043 -- 1x2 3x2 4x2 repeat\n487 x 491 x 499 = 119319383 -- 1x3 3x3 9x2 repeat\n491 x 499 x 503 = 123239527 -- 2x3 3x2 repeat\n499 x 503 x 509 = 127757473 -- 7x4 repeat\n503 x 509 x 521 = 133390067 -- 0x2 3x3 repeat\n509 x 521 x 523 = 138693847 -- 3x2 8x2 repeat\n521 x 523 x 541 = 147413303 -- 1x2 3x3 4x2 repeat\n523 x 541 x 547 = 154769821 -- 1x2 repeat\n541 x 547 x 557 = 164831339 -- 1x2 3x3 repeat\n547 x 557 x 563 = 171534277 -- 1x2 7x3 repeat\n557 x 563 x 569 = 178433279 -- 3x2 7x2 repeat\n563 x 569 x 571 = 182918137 -- 1x3 8x2 repeat\n569 x 571 x 577 = 187466723 -- 6x2 7x2 repeat\n571 x 577 x 587 = 193397129 -- 1x2 3x2 9x3 repeat\n577 x 587 x 593 = 200848507 -- 0x3 8x2 repeat\n587 x 593 x 599 = 208506509 -- 0x3 5x2 repeat\n593 x 599 x 601 = 213479407 -- 4x2 7x2 repeat\n599 x 601 x 607 = 218519393 -- 1x2 3x2 9x2 repeat\n601 x 607 x 613 = 223626691 -- 2x3 6x3 repeat\n607 x 613 x 617 = 229580147 -- 2x2 repeat\n613 x 617 x 619 = 234118799 -- 1x2 9x2 repeat\n617 x 619 x 631 = 240993413 -- 3x2 4x2 9x2 repeat\n619 x 631 x 641
806711
YES it is and here is a list of the firs 1000 prime numbers so just print it out and look at it while your homework.\nhttp://primes.utm.edu/lists/small/1000.txt
313908
The greatest secrets in banks, internet security, commerce and governments are protected by codes built on exteremely large prime numbers. The reason? To our current knowledge, even all the most powerful computers on the earth joined together would need more than billions of years to find out these prime number "keys" by "brute force". Brute force here means writing a computer program to run all possibilities according to an assigned rule.\n\nThats a pretty important function for a number.\n\nIn fact, there is a "milenium problem", where the Clay Mathematics institute offers USD 1 milliom to those that can solve any one of the 7 millenium problems. \n\nAnd one of these problems is the Riemann Hypothesis. \nIt's an exteremely important conjecture about prime numbers that cannot be stated in lay man terms.\nMany experts ( mathematicans ) fear that the "proof" or "disproof" of the Riemann hypothesis may bring out an utterly "new" way of finding "extremely large primes", \ncutting short the work needed earlier by brute force.\nThis more efficient process is feared that it may cut down the workload for identyfying these primes ( or cracking the key you may say ), leading to a catastrophic faiure in security. This is because by cutting the "brute force" workload, one may get to the "guessing" by a shorter time via a computer script or programme based on this "new" way revealed with the proof.\n\nNevertheless, dont fear. Its an extreme longshot that depends on a lot of "if"'s. In fact, contrary to this mathematical myth, the proof of the Riemann Hypothesis might just be "showing the existence" without shedding any light on the behaviour of primes that could be used in the wrong way. \n\nPrime numbers can be found in many other ways describing science. Well, there are 7 colours in a rainbow, etc.\n\nRegards
701564
Prime numbers between through 1 to 100 is\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....
58522
Well, these guys do, and its not just for the 100 thousand dollar prize!! (The Electronic Frontier Foundation is offering a $100,000 award to the first person or group to discover a ten million digit prime number.)\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\n\n\nBtw, (2^30402457)-1 is the largest known prime number!!!
583419
yes..http://primes.utm.edu/curios/page.php/101.html
506986
This is called the twin prime conjecture. The conjecture states that there are an infinite number of pairs of twin primes (p and p+2). It has not been proven there are an infinite number of such primes but it seems almost certain to be true.  While Hardy and Wright note that "the evidence, when examined in detail, appears to justify the conjecture," and Shanks states even more strongly, "the evidence is overwhelming," Hardy and Wright also note that the proof or disproof of conjectures of this type "is at present beyond the resources of mathematics."
841386
The largest known prime, as of September 2006, is 2^32,582,657 − 1 (this number is 9,808,358 digits long); it is the 44th known Mersenne prime. \n\nErastothenes didn't discover any particularly large primes but did invent the first sieve method for finding primes, now known as the Erastothenes sieve. He's better known for being the first person to calculate with reasonable accuracy the size of the Earth.
843926
101 is a prime number. No other number besides 1 can be evenly divided into it.\n\n133 on the other hand, can be broken down into 7*19. This is the prime factorization because both 7 and 19 are prime numbers and cannot be broken down any further.\n\nI hope this helps!