500,309

31 × 16139

Starting at 500,309, the Collatz iteration reaches 1 after 138 steps. The first transition is 1500928; the starting value is odd with 4 positive divisors.

Prime Factor Structure

Factorization String 31 × 16139

Distinct Prime Factors 2

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 4

Divisor Sum (σ) 516,480

Proper Divisor Sum 16,171

Digit Sum / Digital Root 17 (Root: 8)

Adjacent Primes #500299 ← → #500317

Radix Representation

Decimal	500309
Binary	1111010001001010101 (19 bits)
Octal	0o1721125
Hexadecimal	0x7A255

Divisor Catalog (4)

1 31 16,139 500,309

Collatz Trajectory (138 steps to reach 1)

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

500,309 1,500,928 750,464 375,232 187,616 93,808 46,904 23,452 11,726 5,863 17,590 8,795 26,386 13,193 39,580 19,790 9,895 29,686 14,843 44,530 22,265 66,796 33,398 16,699 50,098 25,049 75,148 37,574 18,787 56,362 28,181 84,544 42,272 21,136 10,568 5,284 2,642 1,321 3,964 1,982 991 2,974 1,487 4,462 2,231 6,694 3,347 10,042 5,021 15,064 7,532 3,766 1,883 5,650 2,825 8,476 4,238 2,119 6,358 3,179

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