2,138,565

3 × 5 × 11 × 13 × 997

Starting at 2,138,565, the Collatz iteration reaches 1 after 96 steps. The first transition is 6415696; the starting value is odd with 32 positive divisors.

Prime Factor Structure

Factorization String 3 × 5 × 11 × 13 × 997

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 4,023,936

Proper Divisor Sum 1,885,371

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #2138551 ← → #2138569

Radix Representation

Decimal	2138565
Binary	1000001010000111000101 (22 bits)
Octal	0o10120705
Hexadecimal	0x20A1C5

Divisor Catalog (32)

1 3 5 11 13 15 33 39 55 65 143 165 195 429 715 997 2,145 2,991 4,985 10,967 12,961 14,955 32,901 38,883 54,835 64,805 142,571 164,505 194,415 427,713 712,855 2,138,565

Collatz Trajectory (96 steps to reach 1)

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

2,138,565 6,415,696 3,207,848 1,603,924 801,962 400,981 1,202,944 601,472 300,736 150,368 75,184 37,592 18,796 9,398 4,699 14,098 7,049 21,148 10,574 5,287 15,862 7,931 23,794 11,897 35,692 17,846 8,923 26,770 13,385 40,156 20,078 10,039 30,118 15,059 45,178 22,589 67,768 33,884 16,942 8,471 25,414 12,707 38,122 19,061 57,184 28,592 14,296 7,148 3,574 1,787 5,362 2,681 8,044 4,022 2,011 6,034 3,017 9,052 4,526 2,263

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