3,112,590

2 × 3 × 5 × 13 × 23 × 347

Starting at 3,112,590, the Collatz iteration reaches 1 after 133 steps. The first transition is 1556295; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 5 × 13 × 23 × 347

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 8,418,816

Proper Divisor Sum 5,306,226

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #3112519 ← → #3112609

Radix Representation

Decimal	3112590
Binary	1011110111111010001110 (22 bits)
Octal	0o13677216
Hexadecimal	0x2F7E8E

Divisor Catalog (60 of 64)

1 2 3 5 6 10 13 15 23 26 30 39 46 65 69 78 115 130 138 195 230 299 345 347 390 598 690 694 897 1,041 1,495 1,735 1,794 2,082 2,990 3,470 4,485 4,511 5,205 7,981 8,970 9,022 10,410 13,533 15,962 22,555 23,943 27,066 39,905 45,110 47,886 67,665 79,810 103,753 119,715 135,330 207,506 239,430 311,259 518,765

Collatz Trajectory (133 steps to reach 1)

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

3,112,590 1,556,295 4,668,886 2,334,443 7,003,330 3,501,665 10,504,996 5,252,498 2,626,249 7,878,748 3,939,374 1,969,687 5,909,062 2,954,531 8,863,594 4,431,797 13,295,392 6,647,696 3,323,848 1,661,924 830,962 415,481 1,246,444 623,222 311,611 934,834 467,417 1,402,252 701,126 350,563 1,051,690 525,845 1,577,536 788,768 394,384 197,192 98,596 49,298 24,649 73,948 36,974 18,487 55,462 27,731 83,194 41,597 124,792 62,396 31,198 15,599 46,798 23,399 70,198 35,099 105,298 52,649 157,948 78,974 39,487 118,462

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