8,229,999

3 × 53 × 191 × 271

Starting at 8,229,999, the Collatz iteration reaches 1 after 261 steps. The first transition is 24689998; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 53 × 191 × 271

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 11,280,384

Proper Divisor Sum 3,050,385

Digit Sum / Digital Root 48 (Root: 3)

Adjacent Primes #8229959 ← → #8230003

Radix Representation

Decimal	8229999
Binary	11111011001010001101111 (23 bits)
Octal	0o37312157
Hexadecimal	0x7D946F

Divisor Catalog (16)

1 3 53 159 191 271 573 813 10,123 14,363 30,369 43,089 51,761 155,283 2,743,333 8,229,999

Collatz Trajectory (261 steps to reach 1)

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

8,229,999 24,689,998 12,344,999 37,034,998 18,517,499 55,552,498 27,776,249 83,328,748 41,664,374 20,832,187 62,496,562 31,248,281 93,744,844 46,872,422 23,436,211 70,308,634 35,154,317 105,462,952 52,731,476 26,365,738 13,182,869 39,548,608 19,774,304 9,887,152 4,943,576 2,471,788 1,235,894 617,947 1,853,842 926,921 2,780,764 1,390,382 695,191 2,085,574 1,042,787 3,128,362 1,564,181 4,692,544 2,346,272 1,173,136 586,568 293,284 146,642 73,321 219,964 109,982 54,991 164,974 82,487 247,462 123,731 371,194 185,597 556,792 278,396 139,198 69,599 208,798 104,399 313,198

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