7,856,127

3² × 97 × 8999

Starting at 7,856,127, the Collatz iteration reaches 1 after 261 steps. The first transition is 23568382; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 97 × 8999

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 11,466,000

Proper Divisor Sum 3,609,873

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7856089 ← → #7856161

Radix Representation

Decimal	7856127
Binary	11101111101111111111111 (23 bits)
Octal	0o35757777
Hexadecimal	0x77DFFF

Divisor Catalog (12)

1 3 9 97 291 873 8,999 26,997 80,991 872,903 2,618,709 7,856,127

Collatz Trajectory (261 steps to reach 1)

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

7,856,127 23,568,382 11,784,191 35,352,574 17,676,287 53,028,862 26,514,431 79,543,294 39,771,647 119,314,942 59,657,471 178,972,414 89,486,207 268,458,622 134,229,311 402,687,934 201,343,967 604,031,902 302,015,951 906,047,854 453,023,927 1,359,071,782 679,535,891 2,038,607,674 1,019,303,837 3,057,911,512 1,528,955,756 764,477,878 382,238,939 1,146,716,818 573,358,409 1,720,075,228 860,037,614 430,018,807 1,290,056,422 645,028,211 1,935,084,634 967,542,317 2,902,626,952 1,451,313,476 725,656,738 362,828,369 1,088,485,108 544,242,554 272,121,277 816,363,832 408,181,916 204,090,958 102,045,479 306,136,438 153,068,219 459,204,658 229,602,329 688,806,988 344,403,494 172,201,747 516,605,242 258,302,621 774,907,864 387,453,932

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