2,509,617

3 × 11 × 113 × 673

Starting at 2,509,617, the Collatz iteration reaches 1 after 112 steps. The first transition is 7528852; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 11 × 113 × 673

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 3,688,128

Proper Divisor Sum 1,178,511

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #2509613 ← → #2509621

Radix Representation

Decimal	2509617
Binary	1001100100101100110001 (22 bits)
Octal	0o11445461
Hexadecimal	0x264B31

Divisor Catalog (16)

1 3 11 33 113 339 673 1,243 2,019 3,729 7,403 22,209 76,049 228,147 836,539 2,509,617

Collatz Trajectory (112 steps to reach 1)

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

2,509,617 7,528,852 3,764,426 1,882,213 5,646,640 2,823,320 1,411,660 705,830 352,915 1,058,746 529,373 1,588,120 794,060 397,030 198,515 595,546 297,773 893,320 446,660 223,330 111,665 334,996 167,498 83,749 251,248 125,624 62,812 31,406 15,703 47,110 23,555 70,666 35,333 106,000 53,000 26,500 13,250 6,625 19,876 9,938 4,969 14,908 7,454 3,727 11,182 5,591 16,774 8,387 25,162 12,581 37,744 18,872 9,436 4,718 2,359 7,078 3,539 10,618 5,309 15,928

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