8,323,000

2³ × 5³ × 7 × 29 × 41

Starting at 8,323,000, the Collatz iteration reaches 1 after 160 steps. The first transition is 4161500; the starting value is even with 128 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5^3 × 7 × 29 × 41

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 128

Divisor Sum (σ) 23,587,200

Proper Divisor Sum 15,264,200

Digit Sum / Digital Root 16 (Root: 7)

Adjacent Primes #8322997 ← → #8323009

Radix Representation

Decimal	8323000
Binary	11111101111111110111000 (23 bits)
Octal	0o37577670
Hexadecimal	0x7EFFB8

Divisor Catalog (60 of 128)

1 2 4 5 7 8 10 14 20 25 28 29 35 40 41 50 56 58 70 82 100 116 125 140 145 164 175 200 203 205 232 250 280 287 290 328 350 406 410 500 574 580 700 725 812 820 875 1,000 1,015 1,025 1,148 1,160 1,189 1,400 1,435 1,450 1,624 1,640 1,750 2,030

Collatz Trajectory (160 steps to reach 1)

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

8,323,000 4,161,500 2,080,750 1,040,375 3,121,126 1,560,563 4,681,690 2,340,845 7,022,536 3,511,268 1,755,634 877,817 2,633,452 1,316,726 658,363 1,975,090 987,545 2,962,636 1,481,318 740,659 2,221,978 1,110,989 3,332,968 1,666,484 833,242 416,621 1,249,864 624,932 312,466 156,233 468,700 234,350 117,175 351,526 175,763 527,290 263,645 790,936 395,468 197,734 98,867 296,602 148,301 444,904 222,452 111,226 55,613 166,840 83,420 41,710 20,855 62,566 31,283 93,850 46,925 140,776 70,388 35,194 17,597 52,792

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