2,583,120

2⁴ × 3 × 5 × 47 × 229

Starting at 2,583,120, the Collatz iteration reaches 1 after 112 steps. The first transition is 1291560; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3 × 5 × 47 × 229

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 8,213,760

Proper Divisor Sum 5,630,640

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #2583109 ← → #2583127

Radix Representation

Decimal	2583120
Binary	1001110110101001010000 (22 bits)
Octal	0o11665120
Hexadecimal	0x276A50

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 40 47 48 60 80 94 120 141 188 229 235 240 282 376 458 470 564 687 705 752 916 940 1,128 1,145 1,374 1,410 1,832 1,880 2,256 2,290 2,748 2,820 3,435 3,664 3,760 4,580 5,496 5,640 6,870 9,160 10,763 10,992 11,280 13,740 18,320 21,526

Collatz Trajectory (112 steps to reach 1)

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

2,583,120 1,291,560 645,780 322,890 161,445 484,336 242,168 121,084 60,542 30,271 90,814 45,407 136,222 68,111 204,334 102,167 306,502 153,251 459,754 229,877 689,632 344,816 172,408 86,204 43,102 21,551 64,654 32,327 96,982 48,491 145,474 72,737 218,212 109,106 54,553 163,660 81,830 40,915 122,746 61,373 184,120 92,060 46,030 23,015 69,046 34,523 103,570 51,785 155,356 77,678 38,839 116,518 58,259 174,778 87,389 262,168 131,084 65,542 32,771 98,314

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