7,510,120

2³ × 5 × 191 × 983

Starting at 7,510,120, the Collatz iteration reaches 1 after 85 steps. The first transition is 3755060; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5 × 191 × 983

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 17,003,520

Proper Divisor Sum 9,493,400

Digit Sum / Digital Root 16 (Root: 7)

Adjacent Primes #7510117 ← → #7510127

Radix Representation

Decimal	7510120
Binary	11100101001100001101000 (23 bits)
Octal	0o34514150
Hexadecimal	0x729868

Divisor Catalog (32)

1 2 4 5 8 10 20 40 191 382 764 955 983 1,528 1,910 1,966 3,820 3,932 4,915 7,640 7,864 9,830 19,660 39,320 187,753 375,506 751,012 938,765 1,502,024 1,877,530 3,755,060 7,510,120

Collatz Trajectory (85 steps to reach 1)

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

7,510,120 3,755,060 1,877,530 938,765 2,816,296 1,408,148 704,074 352,037 1,056,112 528,056 264,028 132,014 66,007 198,022 99,011 297,034 148,517 445,552 222,776 111,388 55,694 27,847 83,542 41,771 125,314 62,657 187,972 93,986 46,993 140,980 70,490 35,245 105,736 52,868 26,434 13,217 39,652 19,826 9,913 29,740 14,870 7,435 22,306 11,153 33,460 16,730 8,365 25,096 12,548 6,274 3,137 9,412 4,706 2,353 7,060 3,530 1,765 5,296 2,648 1,324

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