8,029,413

3² × 7 × 233 × 547

Starting at 8,029,413, the Collatz iteration reaches 1 after 186 steps. The first transition is 24088240; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 7 × 233 × 547

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 13,336,128

Proper Divisor Sum 5,306,715

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #8029393 ← → #8029421

Radix Representation

Decimal	8029413
Binary	11110101000010011100101 (23 bits)
Octal	0o36502345
Hexadecimal	0x7A84E5

Divisor Catalog (24)

1 3 7 9 21 63 233 547 699 1,631 1,641 2,097 3,829 4,893 4,923 11,487 14,679 34,461 127,451 382,353 892,157 1,147,059 2,676,471 8,029,413

Collatz Trajectory (186 steps to reach 1)

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

8,029,413 24,088,240 12,044,120 6,022,060 3,011,030 1,505,515 4,516,546 2,258,273 6,774,820 3,387,410 1,693,705 5,081,116 2,540,558 1,270,279 3,810,838 1,905,419 5,716,258 2,858,129 8,574,388 4,287,194 2,143,597 6,430,792 3,215,396 1,607,698 803,849 2,411,548 1,205,774 602,887 1,808,662 904,331 2,712,994 1,356,497 4,069,492 2,034,746 1,017,373 3,052,120 1,526,060 763,030 381,515 1,144,546 572,273 1,716,820 858,410 429,205 1,287,616 643,808 321,904 160,952 80,476 40,238 20,119 60,358 30,179 90,538 45,269 135,808 67,904 33,952 16,976 8,488

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