518,520

2³ × 3 × 5 × 29 × 149

Starting at 518,520, the Collatz iteration reaches 1 after 133 steps. The first transition is 259260; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 29 × 149

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 1,620,000

Proper Divisor Sum 1,101,480

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #518509 ← → #518521

Radix Representation

Decimal	518520
Binary	1111110100101111000 (19 bits)
Octal	0o1764570
Hexadecimal	0x7E978

Divisor Catalog (60 of 64)

1 2 3 4 5 6 8 10 12 15 20 24 29 30 40 58 60 87 116 120 145 149 174 232 290 298 348 435 447 580 596 696 745 870 894 1,160 1,192 1,490 1,740 1,788 2,235 2,980 3,480 3,576 4,321 4,470 5,960 8,642 8,940 12,963 17,284 17,880 21,605 25,926 34,568 43,210 51,852 64,815 86,420 103,704

Collatz Trajectory (133 steps to reach 1)

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

518,520 259,260 129,630 64,815 194,446 97,223 291,670 145,835 437,506 218,753 656,260 328,130 164,065 492,196 246,098 123,049 369,148 184,574 92,287 276,862 138,431 415,294 207,647 622,942 311,471 934,414 467,207 1,401,622 700,811 2,102,434 1,051,217 3,153,652 1,576,826 788,413 2,365,240 1,182,620 591,310 295,655 886,966 443,483 1,330,450 665,225 1,995,676 997,838 498,919 1,496,758 748,379 2,245,138 1,122,569 3,367,708 1,683,854 841,927 2,525,782 1,262,891 3,788,674 1,894,337 5,683,012 2,841,506 1,420,753 4,262,260

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