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Quotation

"I'll show you one more thing about perfect numbers," he said, swinging the branch and drawing his legs under the bench to make more room on the ground. "You can express them as the sum of consecutive natural numbers." 6 = 1 + 2 + 3; 28 = 1 + 2 + 3 + 4 + 5 + 6 + 7; 496 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 === Two is the only even prime. It's the leadoff batter for the infinite team of prime numbers after it. === And, the sum of the prime factors of 714 equals the sum of the prime factors of 715: 714 = 2 × 3 × 7 × 17; 715 = 5 × 11 × 13; 2 + 3 + 7 + 17 = 5 + 11 + 13 = 29. A pair of consecutive whole numbers with these properties is quite rare. There are only 26 such pairs up to 20,000. This one is the Ruth-Aaron pair. Just like prime numbers, they are more rare as the numbers get larger. And 5 and 6 are the smallest pair.