7,741,175

5² × 13 × 23819

Starting at 7,741,175, the Collatz iteration reaches 1 after 98 steps. The first transition is 23223526; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 5^2 × 13 × 23819

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 10,337,880

Proper Divisor Sum 2,596,705

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #7741163 ← → #7741193

Radix Representation

Decimal	7741175
Binary	11101100001111011110111 (23 bits)
Octal	0o35417367
Hexadecimal	0x761EF7

Divisor Catalog (12)

1 5 13 25 65 325 23,819 119,095 309,647 595,475 1,548,235 7,741,175

Collatz Trajectory (98 steps to reach 1)

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

7,741,175 23,223,526 11,611,763 34,835,290 17,417,645 52,252,936 26,126,468 13,063,234 6,531,617 19,594,852 9,797,426 4,898,713 14,696,140 7,348,070 3,674,035 11,022,106 5,511,053 16,533,160 8,266,580 4,133,290 2,066,645 6,199,936 3,099,968 1,549,984 774,992 387,496 193,748 96,874 48,437 145,312 72,656 36,328 18,164 9,082 4,541 13,624 6,812 3,406 1,703 5,110 2,555 7,666 3,833 11,500 5,750 2,875 8,626 4,313 12,940 6,470 3,235 9,706 4,853 14,560 7,280 3,640 1,820 910 455 1,366

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