λ
Harmonic Matrix

5,000,657

5000657
Deficient Odd Prime

5,000,657 has digital root 5. The neighboring primes are 5000651 and 5000687; its proper-divisor sum differs from the starting integer by -5,000,656.

Prime Factor Structure

Factorization String 5000657
Distinct Prime Factors 1
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 2
Divisor Sum (σ) 5,000,658
Proper Divisor Sum 1
Digit Sum / Digital Root 23 (Root: 5)
Adjacent Primes #5000651 ← → #5000687

Radix Representation

Decimal 5000657
Binary 10011000100110111010001 (23 bits)
Octal 0o23046721
Hexadecimal 0x4C4DD1

Divisor Catalog (2)

1 5,000,657

Collatz Trajectory (113 steps to reach 1)

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

5,000,657 15,001,972 7,500,986 3,750,493 11,251,480 5,625,740 2,812,870 1,406,435 4,219,306 2,109,653 6,328,960 3,164,480 1,582,240 791,120 395,560 197,780 98,890 49,445 148,336 74,168 37,084 18,542 9,271 27,814 13,907 41,722 20,861 62,584 31,292 15,646 7,823 23,470 11,735 35,206 17,603 52,810 26,405 79,216 39,608 19,804 9,902 4,951 14,854 7,427 22,282 11,141 33,424 16,712 8,356 4,178 2,089 6,268 3,134 1,567 4,702 2,351 7,054 3,527 10,582 5,291

More profiles

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