7,712,577

3⁵ × 17 × 1867

Starting at 7,712,577, the Collatz iteration reaches 1 after 124 steps. The first transition is 23137732; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 3^5 × 17 × 1867

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 12,239,136

Proper Divisor Sum 4,526,559

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7712563 ← → #7712581

Radix Representation

Decimal	7712577
Binary	11101011010111101000001 (23 bits)
Octal	0o35327501
Hexadecimal	0x75AF41

Divisor Catalog (24)

Collatz Trajectory (124 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

7,712,577 23,137,732 11,568,866 5,784,433 17,353,300 8,676,650 4,338,325 13,014,976 6,507,488 3,253,744 1,626,872 813,436 406,718 203,359 610,078 305,039 915,118 457,559 1,372,678 686,339 2,059,018 1,029,509 3,088,528 1,544,264 772,132 386,066 193,033 579,100 289,550 144,775 434,326 217,163 651,490 325,745 977,236 488,618 244,309 732,928 366,464 183,232 91,616 45,808 22,904 11,452 5,726 2,863 8,590 4,295 12,886 6,443 19,330 9,665 28,996 14,498 7,249 21,748 10,874 5,437 16,312 8,156

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