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21. ONJava.com: Web Services And The Search For Really Big Prime Numbers [Aug. 29, 2
    Finally, again from the Euler theorem, perfect numbers are related to prime numbersin that an even perfect number can be expressed in the form n = 2 k1 (2 k  
    http://www.onjava.com/pub/a/onjava/2002/08/28/wsdc.html?page=2

22. Prime Page References
    HS76 M. Hausmann and H. Shapiro, perfect ideals over the gaussian integers MR 263684Huxley72 MN Huxley, The distribution of prime numbers, Oxford University  
    http://www.utm.edu/research/primes/references/refs.cgi/refs.cgi?range=h

23. Prime Factorizations, Perfect Squares And Irrational Numbers
    prime Factorizations, perfect Squares and Irrational numbers. About this document prime Factorizations, perfect Squares and Irrational numbers  
    http://bolzano.sf.edu/math_120/primefactor/

24. Puzzle 35.- 1999 And The Perfect Numbers
    be written as P = (1/2)(M)(M+1), where M is a Mersenne prime (2^p hold, and consequently6 != 1 (mod 9). However, this must hold for all other perfect numbers.  
    http://www.primepuzzles.net/puzzles/puzz_035.htm

25. Prime Queen Attacking Problem
    largest one for which we have found a perfect solution. the Queen sits on one of thetwo central odd numbers. and if the Queen also attacked the prime 2, then  
    http://users.aol.com/s6sj7gt/primeq.htm

26. Perfect, Amicable And Sociable Numbers
    multiplied by a squarefree number relatively prime to every member of the cycle,so there are an infinite number of exponential perfect numbers, of exponential  
    http://xraysgi.ims.uconn.edu/amicable.html

27. Perfect Numbers
    Harry J. Smith's pages of the mathematics behind perfection, aliquot sequences and Mersenne numbers .Category Science Math Number Theory Factoring perfect numbersperfect numbers. Select a Subtitle What is a perfect Number? My Talk on AliquotParts Mersenne primes The GREAT Internet Mersenne prime Search GIMPS Plot of  
    http://pw1.netcom.com/~hjsmith/Perfect.html

28. Resources
    prime Curios collection of curiosities, wonders and trivia related to prime numbers.The perfect Number Journey (6, 28, ) An integer is perfect if it equals  
    http://michaelshepperd.tripod.com/resources/prime.html

29. Number Theory
    How are the prime numbers distributed? What is the largest known prime number? Whatare perfect, abundant, deficient, Mersenne, Fermat, and sublime numbers?  
    http://mail.colonial.net/~abeckwith/numthry.html

30. Glossary-P
    For example, 6 is a perfect number because the sum of its proper factors is 1 + 2+ 3 = 6. See also abundant The first five prime numbers are 2, 3, 5, 7, and 11  
    http://www.kent.k12.wa.us/curriculum/math/edmath/glossary/glossary_P.html

31. Math Trek : A Perfect Collaboration, Science News Online, Jan. 18, 2003
    and these numbers figure prominently in the search for the largest known prime.Every Mersenne number uncovered automatically leads to a new perfect number.  
    http://www.sciencenews.org/20030118/mathtrek.asp

32. StudyWorks! Online : Perfect Numbers
    If you look closely at the method we used for computing perfect numbers, you willnotice that So if n is an integer and 2 n 1 is prime then is a perfect number  
    http://www.studyworksonline.com/cda/content/article/0,,EXP1720_NAV2-95_SAR1724,0

33. Mathlinks.info - Numbers And Constants
    The perfect Number Journey Tutorial (O Heng); perfect numbers - Article (MacTutor theFirst 1000 Integers - Pages (SOS Math); prime numbers - Article (MacTutor  
    http://www.mathlinks.info/em026_numbers_and_constants.htm

34. MGMSI | Instructor Manual | Course Outlines | Number Sense
    special classes of prime and composite numbers (ie, Mersenne primes, abundantnumbers, deficient numbers, perfect numbers, and relatively prime numbers).  
    http://www.mgmsi.usg.edu/instruct/manual/courses/num_sense/homepg.htm

35. Www.math.niu.edu/~rusin/known-math/98/perfect
    there are fairly efficient ways to determine whether a number 2^p 1 is prime,so very large primen numbers, and thus very large perfect numbers, have been  
    http://www.math.niu.edu/~rusin/known-math/98/perfect

36. Department Of Mathematics And Statistics - News and Events
    of the subject of distribution of primes, and then I'll discuss a new connectionof certain prime forms (especially quadratic primes) and odd perfect numbers.  
    http://www.math.ucalgary.ca/events/index.php3?newstypeid=12&Which=380

37. Number Theory And Arithmetic In The Pentagon
    numbers, Robert W. Prielipp 37, 1, 1618, The Relationship of Pascal's Triangleand perfect numbers, Robert A. Antol 39, 2, 94-98, On prime Powers Which  
    http://www.kme.eku.edu/numthe.htm

38. Welcome To The Sanford Circles
    including counting from 1 to 100 in 1's, 2's, 3's and 5's, the large colorful (2'x3')poster contains the Times Tables, prime numbers, perfect Squares, perfect  
    http://www.ic-2000.com/sanford/

39. PBS TeacherSource - Mathline - Middle School Math Project
    Objective. Students will use a game setting to identify the properties of prime,composite, abundant, deficient and perfect numbers. Overview of the Lesson.  
    http://www.pbs.org/teachersource/mathline/lessonplans/msmp/factor/factor_procedu

40. Math In The Media 1002
    The proof is worth $10,000 (put up by fellow perfectgraph aficionado George Johnsongives us a meditation on prime numbers and their distribution ( From Here  
    http://www.ams.org/new-in-math/10-2002-media.html

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