7,937,727

3 × 7 × 431 × 877

Starting at 7,937,727, the Collatz iteration reaches 1 after 173 steps. The first transition is 23813182; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 7 × 431 × 877

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 12,137,472

Proper Divisor Sum 4,199,745

Digit Sum / Digital Root 42 (Root: 6)

Adjacent Primes #7937719 ← → #7937731

Radix Representation

Decimal	7937727
Binary	11110010001111010111111 (23 bits)
Octal	0o36217277
Hexadecimal	0x791EBF

Divisor Catalog (16)

1 3 7 21 431 877 1,293 2,631 3,017 6,139 9,051 18,417 377,987 1,133,961 2,645,909 7,937,727

Collatz Trajectory (173 steps to reach 1)

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

7,937,727 23,813,182 11,906,591 35,719,774 17,859,887 53,579,662 26,789,831 80,369,494 40,184,747 120,554,242 60,277,121 180,831,364 90,415,682 45,207,841 135,623,524 67,811,762 33,905,881 101,717,644 50,858,822 25,429,411 76,288,234 38,144,117 114,432,352 57,216,176 28,608,088 14,304,044 7,152,022 3,576,011 10,728,034 5,364,017 16,092,052 8,046,026 4,023,013 12,069,040 6,034,520 3,017,260 1,508,630 754,315 2,262,946 1,131,473 3,394,420 1,697,210 848,605 2,545,816 1,272,908 636,454 318,227 954,682 477,341 1,432,024 716,012 358,006 179,003 537,010 268,505 805,516 402,758 201,379 604,138 302,069

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