7,641,592

2³ × 7 × 61 × 2237

Starting at 7,641,592, the Collatz iteration reaches 1 after 129 steps. The first transition is 3820796; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 7 × 61 × 2237

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 16,650,720

Proper Divisor Sum 9,009,128

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #7641533 ← → #7641611

Radix Representation

Decimal	7641592
Binary	11101001001100111111000 (23 bits)
Octal	0o35114770
Hexadecimal	0x7499F8

Divisor Catalog (32)

1 2 4 7 8 14 28 56 61 122 244 427 488 854 1,708 2,237 3,416 4,474 8,948 15,659 17,896 31,318 62,636 125,272 136,457 272,914 545,828 955,199 1,091,656 1,910,398 3,820,796 7,641,592

Collatz Trajectory (129 steps to reach 1)

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

7,641,592 3,820,796 1,910,398 955,199 2,865,598 1,432,799 4,298,398 2,149,199 6,447,598 3,223,799 9,671,398 4,835,699 14,507,098 7,253,549 21,760,648 10,880,324 5,440,162 2,720,081 8,160,244 4,080,122 2,040,061 6,120,184 3,060,092 1,530,046 765,023 2,295,070 1,147,535 3,442,606 1,721,303 5,163,910 2,581,955 7,745,866 3,872,933 11,618,800 5,809,400 2,904,700 1,452,350 726,175 2,178,526 1,089,263 3,267,790 1,633,895 4,901,686 2,450,843 7,352,530 3,676,265 11,028,796 5,514,398 2,757,199 8,271,598 4,135,799 12,407,398 6,203,699 18,611,098 9,305,549 27,916,648 13,958,324 6,979,162 3,489,581 10,468,744

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