What are the first 10 perfect numbers?
Perfect numbers have fascinated mathematicians for centuries. These are positive integers that are equal to the sum of their proper divisors, excluding the number itself. In other words, a perfect number is the sum of its factors, excluding the number itself. The first 10 perfect numbers are as follows:
1. 6: The smallest perfect number, 6 is the sum of its proper divisors 1, 2, and 3.
2. 28: The next perfect number, 28, is the sum of its proper divisors 1, 2, 4, 7, and 14.
3. 496: 496 is the sum of its proper divisors 1, 2, 4, 8, 16, 31, 62, 124, and 248.
4. 8128: The fourth perfect number, 8128, is the sum of its proper divisors 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, and 1016.
5. 33550336: The fifth perfect number, 33550336, is the sum of its proper divisors 1, 2, 4, 8, 16, 3355032, and 6717516.
6. 8589869056: The sixth perfect number, 8589869056, is the sum of its proper divisors 1, 2, 4, 8, 16, 429496729, 858986905, and 1717973810.
7. 137438691328: The seventh perfect number, 137438691328, is the sum of its proper divisors 1, 2, 4, 8, 16, 274877906, 549755812, 1099511614, and 2199023226.
8. 2305843008139952128: The eighth perfect number, 2305843008139952128, is the sum of its proper divisors 1, 2, 4, 8, 16, 230584300813995212, and 460116601567994104.
9. 2658455991569831744654692615953842176: The ninth perfect number, 2658455991569831744654692615953842176, is the sum of its proper divisors 1, 2, 4, 8, 16, 532428598078496796, 1064857196156993952, and 2129714392313987904.
10. 3215031751×2^127−1: The tenth perfect number, 3215031751×2^127−1, is the sum of its proper divisors 1, 2, 4, 8, 16, 3215031751, 6430063502, 12860127004, 25620254008, 51240508016, and 102880100032.
These numbers have intrigued mathematicians since ancient times, and their discovery has led to the development of various mathematical theories and algorithms. The search for new perfect numbers continues to be a subject of interest in the field of mathematics.
