515,613

3 × 7 × 43 × 571

Starting at 515,613, the Collatz iteration reaches 1 after 102 steps. The first transition is 1546840; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 7 × 43 × 571

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 805,376

Proper Divisor Sum 289,763

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #515611 ← → #515621

Radix Representation

Decimal	515613
Binary	1111101111000011101 (19 bits)
Octal	0o1757035
Hexadecimal	0x7DE1D

Divisor Catalog (16)

1 3 7 21 43 129 301 571 903 1,713 3,997 11,991 24,553 73,659 171,871 515,613

Collatz Trajectory (102 steps to reach 1)

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

515,613 1,546,840 773,420 386,710 193,355 580,066 290,033 870,100 435,050 217,525 652,576 326,288 163,144 81,572 40,786 20,393 61,180 30,590 15,295 45,886 22,943 68,830 34,415 103,246 51,623 154,870 77,435 232,306 116,153 348,460 174,230 87,115 261,346 130,673 392,020 196,010 98,005 294,016 147,008 73,504 36,752 18,376 9,188 4,594 2,297 6,892 3,446 1,723 5,170 2,585 7,756 3,878 1,939 5,818 2,909 8,728 4,364 2,182 1,091 3,274

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