8,000,991

3³ × 37 × 8009

Starting at 8,000,991, the Collatz iteration reaches 1 after 142 steps. The first transition is 24002974; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3^3 × 37 × 8009

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 12,175,200

Proper Divisor Sum 4,174,209

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #8000989 ← → #8001029

Radix Representation

Decimal	8000991
Binary	11110100001010111011111 (23 bits)
Octal	0o36412737
Hexadecimal	0x7A15DF

Divisor Catalog (16)

1 3 9 27 37 111 333 999 8,009 24,027 72,081 216,243 296,333 888,999 2,666,997 8,000,991

Collatz Trajectory (142 steps to reach 1)

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

8,000,991 24,002,974 12,001,487 36,004,462 18,002,231 54,006,694 27,003,347 81,010,042 40,505,021 121,515,064 60,757,532 30,378,766 15,189,383 45,568,150 22,784,075 68,352,226 34,176,113 102,528,340 51,264,170 25,632,085 76,896,256 38,448,128 19,224,064 9,612,032 4,806,016 2,403,008 1,201,504 600,752 300,376 150,188 75,094 37,547 112,642 56,321 168,964 84,482 42,241 126,724 63,362 31,681 95,044 47,522 23,761 71,284 35,642 17,821 53,464 26,732 13,366 6,683 20,050 10,025 30,076 15,038 7,519 22,558 11,279 33,838 16,919 50,758

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