8,021,958

2 × 3 × 7 × 389 × 491

Starting at 8,021,958, the Collatz iteration reaches 1 after 93 steps. The first transition is 4010979; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 389 × 491

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 18,420,480

Proper Divisor Sum 10,398,522

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #8021941 ← → #8021969

Radix Representation

Decimal	8021958
Binary	11110100110011111000110 (23 bits)
Octal	0o36463706
Hexadecimal	0x7A67C6

Divisor Catalog (32)

1 2 3 6 7 14 21 42 389 491 778 982 1,167 1,473 2,334 2,723 2,946 3,437 5,446 6,874 8,169 10,311 16,338 20,622 190,999 381,998 572,997 1,145,994 1,336,993 2,673,986 4,010,979 8,021,958

Collatz Trajectory (93 steps to reach 1)

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

8,021,958 4,010,979 12,032,938 6,016,469 18,049,408 9,024,704 4,512,352 2,256,176 1,128,088 564,044 282,022 141,011 423,034 211,517 634,552 317,276 158,638 79,319 237,958 118,979 356,938 178,469 535,408 267,704 133,852 66,926 33,463 100,390 50,195 150,586 75,293 225,880 112,940 56,470 28,235 84,706 42,353 127,060 63,530 31,765 95,296 47,648 23,824 11,912 5,956 2,978 1,489 4,468 2,234 1,117 3,352 1,676 838 419 1,258 629 1,888 944 472 236

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