515,513

83 × 6211

Starting at 515,513, the Collatz iteration reaches 1 after 195 steps. The first transition is 1546540; the starting value is odd with 4 positive divisors.

Prime Factor Structure

Factorization String 83 × 6211

Distinct Prime Factors 2

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 4

Divisor Sum (σ) 521,808

Proper Divisor Sum 6,295

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #515507 ← → #515519

Radix Representation

Decimal	515513
Binary	1111101110110111001 (19 bits)
Octal	0o1756671
Hexadecimal	0x7DDB9

Divisor Catalog (4)

1 83 6,211 515,513

Collatz Trajectory (195 steps to reach 1)

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

515,513 1,546,540 773,270 386,635 1,159,906 579,953 1,739,860 869,930 434,965 1,304,896 652,448 326,224 163,112 81,556 40,778 20,389 61,168 30,584 15,292 7,646 3,823 11,470 5,735 17,206 8,603 25,810 12,905 38,716 19,358 9,679 29,038 14,519 43,558 21,779 65,338 32,669 98,008 49,004 24,502 12,251 36,754 18,377 55,132 27,566 13,783 41,350 20,675 62,026 31,013 93,040 46,520 23,260 11,630 5,815 17,446 8,723 26,170 13,085 39,256 19,628

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