7,865,002

2 × 1777 × 2213

Starting at 7,865,002, the Collatz iteration reaches 1 after 186 steps. The first transition is 3932501; the starting value is even with 8 positive divisors.

Prime Factor Structure

Factorization String 2 × 1777 × 2213

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 11,809,476

Proper Divisor Sum 3,944,474

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #7864991 ← → #7865009

Radix Representation

Decimal	7865002
Binary	11110000000001010101010 (23 bits)
Octal	0o36001252
Hexadecimal	0x7802AA

Divisor Catalog (8)

1 2 1,777 2,213 3,554 4,426 3,932,501 7,865,002

Collatz Trajectory (186 steps to reach 1)

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

7,865,002 3,932,501 11,797,504 5,898,752 2,949,376 1,474,688 737,344 368,672 184,336 92,168 46,084 23,042 11,521 34,564 17,282 8,641 25,924 12,962 6,481 19,444 9,722 4,861 14,584 7,292 3,646 1,823 5,470 2,735 8,206 4,103 12,310 6,155 18,466 9,233 27,700 13,850 6,925 20,776 10,388 5,194 2,597 7,792 3,896 1,948 974 487 1,462 731 2,194 1,097 3,292 1,646 823 2,470 1,235 3,706 1,853 5,560 2,780 1,390

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