8,398,221

3 × 13 × 17 × 53 × 239

Starting at 8,398,221, the Collatz iteration reaches 1 after 230 steps. The first transition is 25194664; the starting value is odd with 32 positive divisors.

Prime Factor Structure

Factorization String 3 × 13 × 17 × 53 × 239

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 13,063,680

Proper Divisor Sum 4,665,459

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #8398217 ← → #8398231

Radix Representation

Decimal	8398221
Binary	100000000010010110001101 (24 bits)
Octal	0o40022615
Hexadecimal	0x80258D

Divisor Catalog (32)

1 3 13 17 39 51 53 159 221 239 663 689 717 901 2,067 2,703 3,107 4,063 9,321 11,713 12,189 12,667 35,139 38,001 52,819 158,457 164,671 215,339 494,013 646,017 2,799,407 8,398,221

Collatz Trajectory (230 steps to reach 1)

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

8,398,221 25,194,664 12,597,332 6,298,666 3,149,333 9,448,000 4,724,000 2,362,000 1,181,000 590,500 295,250 147,625 442,876 221,438 110,719 332,158 166,079 498,238 249,119 747,358 373,679 1,121,038 560,519 1,681,558 840,779 2,522,338 1,261,169 3,783,508 1,891,754 945,877 2,837,632 1,418,816 709,408 354,704 177,352 88,676 44,338 22,169 66,508 33,254 16,627 49,882 24,941 74,824 37,412 18,706 9,353 28,060 14,030 7,015 21,046 10,523 31,570 15,785 47,356 23,678 11,839 35,518 17,759 53,278

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