Search results
Results from the WOW.Com Content Network
[7] [8] [9] It is widely believed, [10] but not proven, that no odd perfect numbers exist; numerous restrictive conditions have been proven, [10] including a lower bound of 10 1500. [11] The following is a list of all 52 currently known (as of January 2025) Mersenne primes and corresponding perfect numbers, along with their exponents p.
Squares of odd numbers are odd, and are congruent to 1 modulo 8, since (2n + 1) 2 = 4n(n + 1) + 1, and n(n + 1) is always even. In other words, all odd square numbers have a remainder of 1 when divided by 8. Every odd perfect square is a centered octagonal number. The difference between any two odd perfect squares is a multiple of 8.
Illustration of the perfect number status of the number 6. In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number.
The first: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 (sequence A005843 in the OEIS). An odd number does not have the prime factor 2. The first: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 (sequence A005408 in the OEIS). All integers are either even or odd. A square has even multiplicity for all prime factors (it is of the form a 2 for some a).
The palindromic prime 10 150006 + 7 426 247 × 10 75 000 + 1 is a 10-happy prime with 150 007 digits because the many 0s do not contribute to the sum of squared digits, and 1 2 + 7 2 + 4 2 + 2 2 + 6 2 + 2 2 + 4 2 + 7 2 + 1 2 = 176, which is a 10-happy number. Paul Jobling discovered the prime in 2005.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The only perfect 10-squares published in any language to date have been constructed in Latin and English, and perfect 11-squares have been created in Latin as well. [11] Perfect 9-squares have been constructed in French, [12] while perfect squares of at least order 8 have been constructed in Italian and Spanish. [13]