λ
Harmonic Matrix

8,428,421

8428421
Deficient Odd Prime

8,428,421 has digital root 2. The neighboring primes are 8428417 and 8428423; its proper-divisor sum differs from the starting integer by -8,428,420.

Prime Factor Structure

Factorization String 8428421
Distinct Prime Factors 1
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 2
Divisor Sum (σ) 8,428,422
Proper Divisor Sum 1
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #8428417 ← → #8428423

Radix Representation

Decimal 8428421
Binary 100000001001101110000101 (24 bits)
Octal 0o40115605
Hexadecimal 0x809B85

Divisor Catalog (2)

Collatz Trajectory (168 steps to reach 1)

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

8,428,421 25,285,264 12,642,632 6,321,316 3,160,658 1,580,329 4,740,988 2,370,494 1,185,247 3,555,742 1,777,871 5,333,614 2,666,807 8,000,422 4,000,211 12,000,634 6,000,317 18,000,952 9,000,476 4,500,238 2,250,119 6,750,358 3,375,179 10,125,538 5,062,769 15,188,308 7,594,154 3,797,077 11,391,232 5,695,616 2,847,808 1,423,904 711,952 355,976 177,988 88,994 44,497 133,492 66,746 33,373 100,120 50,060 25,030 12,515 37,546 18,773 56,320 28,160 14,080 7,040 3,520 1,760 880 440 220 110 55 166 83 250

More profiles

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