Jlpe's Number Recreations Page Features original number recreations by the author, such as generalized perfect numbers, digital diversio Category Science Math Recreationsjlpe's number recreations page. The concept of number is the obviousdistinction between the beast and man. Thanks to number, the http://www.geocities.com/windmill96/numrecreations.html
Puzzle 111. Spoof Odd Perfect Numbers On the contrary, as you know, there are many even perfect numbers,at least as many as Mersenne prime numbers (38 at the moment). http://www.primepuzzles.net/puzzles/puzz_111.htm
Prime Numbers rules to knock out a large proportion of numbers which are not prime, eg no primenumber can end a number as the difference of two perfect squares because http://dev1.epsb.edmonton.ab.ca/math14_Jim/java/prime/sgprime.htm
Unsolved Problems It can be shown that p must be prime for (*) to be prime. As of December 2002,39 Mersenne primes are known. There are thus 39 known even perfect numbers. http://www.math.utah.edu/~alfeld/math/conjectures.html
Message 46 Containing Perfect, Out The fact that numbers of this form (last factor a mersenneprime) are perfect wasknown by the ancient greeks, but the other way round is not obvious to see. http://pw1.netcom.com/~hjsmith/Perfect/46Out.html
Perfect Number -- From MathWorld intimately connected with a class of numbers known as Mersenne primes. This can bedemonstrated by considering a perfect number P of the form where q is prime. http://mathworld.wolfram.com/PerfectNumber.html
Odd Perfect Number -- From MathWorld Odd perfect numbers. Math. Proc. Cambridge Philos. Soc. 115, 191196, 1994. Iannucci,D. E. The Second Largest prime Divisor of an Odd perfect Number Exceeds http://mathworld.wolfram.com/OddPerfectNumber.html
Perfect Numbers Most numbers do not fit this description. At the heart of every perfectnumber is a Mersenne prime. All of the other divisors are http://www.grc.nasa.gov/WWW/K-12/Numbers/Math/Mathematical_Thinking/prfctno.htm
Perfect Numbers expression 2 n 1 are known as Mersenne numbers, named after to Euclid, you can usethat Mersenne prime to automatically find a perfect number. http://66.137.204.220/plethorama/perfect.htm
VACETS Technical Column - Tc48 They do know, however, that all even perfect numbers have a direct relationshipto Mersenne primes, P = 2^(p1)*(2^p-1) where 2^p-1 is a Mersenne prime. http://www.vacets.org/tc/tc48.html
InterMath | Investigations | Number Concept Historical References *perfect numbers *prime numbers *Fermat's last theorem *Babylonianand Egyptian mathematics Mathematicians *Christian Goldbach *Peirre de http://www.intermath-uga.gatech.edu/topics/nmcncept/integers/links.htm
Perfect Numbers for odd perfect numbers, Math. Comput., 57(1991), 857868. MD Sayers, An improvedlower bound for the total number of prime factors of an odd perfect number, M http://www.math.swt.edu/~haz/prob_sets/notes/node13.html
Sublime Numbers Assuming there are no odd perfect numbers, there can be no more even sublime numbersunless there are other (presently unknown) Mersenne prime exponents that http://www.mathpages.com/home/kmath202/kmath202.htm
Sci.math FAQ: Unsolved Problems Furthermore, the prime occurring to an odd power must itself be congruent to 1 mod4. A sketch It has been shown that there are no odd perfect numbers 10^(300 http://isc.faqs.org/faqs/sci-math-faq/unsolvedproblems/
Science News Online, Ivars Peterson's MathTrek (7/4/98): Prime Talent What's the smallest prime the sum of whose digits is perfect? The prime 1999 alsocomes up in another context 1999 How many convenience store numbers are there http://www.sciencenews.org/sn_arc98/7_4_98/mathland.htm
StudyWorks! Online : Perfect Numbers How many perfect numbers are there? The number, 2 n 1, if it is prime, is calleda Mersenne prime after Marin Mersenne, a seventeenth century French monk http://www.studyworksonline.com/cda/content/article/0,,EXP1720_NAV2-95_SAR1727,0
Valentin Vornicu's MathLinks z . Prove that if p 1 , p 2 , , p n are the first n prime numbersthen p 1 p 2 p n ±1 cannot be a perfect square. For which http://www.mathlinks.go.ro/nthproblems.htm
Prime Numbers - Mental Arithmetic Under Pressure! prime numbers. Story. The perfect place to play with your friends (the socialites!), to evaluate your knowledge (the anguished!) , to cultivate your mind (the http://www.cosmoquiz.com/en/prime_numbers_game.html
F. Conjectures (Math 413, Number Theory) A collection of easily stated conjectures which are still open. Each conjecture is stated along with Category Science Math Number Theory Open Problems Thm M n is prime implies that 2 n 1 (2 n -1) is perfect. (Euclid); All evenperfect numbers are derived from Mersenne primes in this way. (Euler). http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html
Unlucky 13 By Shyam Sunder Gupta of many countries is designated as prime MINISTER containing In Japan, the numbers4 and 9 are considered represented as sum of these two perfect squares but http://www.shyamsundergupta.com/unlucky13.htm