6,476,478

2 × 3 × 23 × 71 × 661

Starting at 6,476,478, the Collatz iteration reaches 1 after 165 steps. The first transition is 3238239; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 23 × 71 × 661

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 13,727,232

Proper Divisor Sum 7,250,754

Digit Sum / Digital Root 42 (Root: 6)

Adjacent Primes #6476471 ← → #6476497

Radix Representation

Decimal	6476478
Binary	11000101101001010111110 (23 bits)
Octal	0o30551276
Hexadecimal	0x62D2BE

Divisor Catalog (32)

1 2 3 6 23 46 69 71 138 142 213 426 661 1,322 1,633 1,983 3,266 3,966 4,899 9,798 15,203 30,406 45,609 46,931 91,218 93,862 140,793 281,586 1,079,413 2,158,826 3,238,239 6,476,478

Collatz Trajectory (165 steps to reach 1)

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

6,476,478 3,238,239 9,714,718 4,857,359 14,572,078 7,286,039 21,858,118 10,929,059 32,787,178 16,393,589 49,180,768 24,590,384 12,295,192 6,147,596 3,073,798 1,536,899 4,610,698 2,305,349 6,916,048 3,458,024 1,729,012 864,506 432,253 1,296,760 648,380 324,190 162,095 486,286 243,143 729,430 364,715 1,094,146 547,073 1,641,220 820,610 410,305 1,230,916 615,458 307,729 923,188 461,594 230,797 692,392 346,196 173,098 86,549 259,648 129,824 64,912 32,456 16,228 8,114 4,057 12,172 6,086 3,043 9,130 4,565 13,696 6,848

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