λ
Harmonic Matrix

8,115,089

41 × 43 × 4603
Deficient Odd Composite

8,115,089 has digital root 5. The neighboring primes are 8115083 and 8115101; its proper-divisor sum differs from the starting integer by -7,721,986.

Prime Factor Structure

Factorization String 41 × 43 × 4603
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 8,508,192
Proper Divisor Sum 393,103
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #8115083 ← → #8115101

Radix Representation

Decimal 8115089
Binary 11110111101001110010001 (23 bits)
Octal 0o36751621
Hexadecimal 0x7BD391

Divisor Catalog (8)

1 41 43 1,763 4,603 188,723 197,929 8,115,089

Collatz Trajectory (137 steps to reach 1)

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

8,115,089 24,345,268 12,172,634 6,086,317 18,258,952 9,129,476 4,564,738 2,282,369 6,847,108 3,423,554 1,711,777 5,135,332 2,567,666 1,283,833 3,851,500 1,925,750 962,875 2,888,626 1,444,313 4,332,940 2,166,470 1,083,235 3,249,706 1,624,853 4,874,560 2,437,280 1,218,640 609,320 304,660 152,330 76,165 228,496 114,248 57,124 28,562 14,281 42,844 21,422 10,711 32,134 16,067 48,202 24,101 72,304 36,152 18,076 9,038 4,519 13,558 6,779 20,338 10,169 30,508 15,254 7,627 22,882 11,441 34,324 17,162 8,581

More profiles

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