7,921,864

2³ × 17 × 31 × 1879

Starting at 7,921,864, the Collatz iteration reaches 1 after 168 steps. The first transition is 3960932; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 17 × 31 × 1879

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 16,243,200

Proper Divisor Sum 8,321,336

Digit Sum / Digital Root 37 (Root: 1)

Adjacent Primes #7921861 ← → #7921873

Radix Representation

Decimal	7921864
Binary	11110001110000011001000 (23 bits)
Octal	0o36160310
Hexadecimal	0x78E0C8

Divisor Catalog (32)

1 2 4 8 17 31 34 62 68 124 136 248 527 1,054 1,879 2,108 3,758 4,216 7,516 15,032 31,943 58,249 63,886 116,498 127,772 232,996 255,544 465,992 990,233 1,980,466 3,960,932 7,921,864

Collatz Trajectory (168 steps to reach 1)

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

7,921,864 3,960,932 1,980,466 990,233 2,970,700 1,485,350 742,675 2,228,026 1,114,013 3,342,040 1,671,020 835,510 417,755 1,253,266 626,633 1,879,900 939,950 469,975 1,409,926 704,963 2,114,890 1,057,445 3,172,336 1,586,168 793,084 396,542 198,271 594,814 297,407 892,222 446,111 1,338,334 669,167 2,007,502 1,003,751 3,011,254 1,505,627 4,516,882 2,258,441 6,775,324 3,387,662 1,693,831 5,081,494 2,540,747 7,622,242 3,811,121 11,433,364 5,716,682 2,858,341 8,575,024 4,287,512 2,143,756 1,071,878 535,939 1,607,818 803,909 2,411,728 1,205,864 602,932 301,466

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