6,727,721

7 × 11² × 13² × 47

6,727,721 has digital root 5. The neighboring primes are 6727717 and 6727741; its proper-divisor sum differs from the starting integer by -4,109,266.

Prime Factor Structure

Factorization String 7 × 11^2 × 13^2 × 47

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 9,346,176

Proper Divisor Sum 2,618,455

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #6727717 ← → #6727741

Radix Representation

Decimal	6727721
Binary	11001101010100000101001 (23 bits)
Octal	0o31524051
Hexadecimal	0x66A829

Divisor Catalog (36)

1 7 11 13 47 77 91 121 143 169 329 517 611 847 1,001 1,183 1,573 1,859 3,619 4,277 5,687 6,721 7,943 11,011 13,013 20,449 39,809 47,047 55,601 73,931 87,373 143,143 517,517 611,611 961,103 6,727,721

Collatz Trajectory (284 steps to reach 1)

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

6,727,721 20,183,164 10,091,582 5,045,791 15,137,374 7,568,687 22,706,062 11,353,031 34,059,094 17,029,547 51,088,642 25,544,321 76,632,964 38,316,482 19,158,241 57,474,724 28,737,362 14,368,681 43,106,044 21,553,022 10,776,511 32,329,534 16,164,767 48,494,302 24,247,151 72,741,454 36,370,727 109,112,182 54,556,091 163,668,274 81,834,137 245,502,412 122,751,206 61,375,603 184,126,810 92,063,405 276,190,216 138,095,108 69,047,554 34,523,777 103,571,332 51,785,666 25,892,833 77,678,500 38,839,250 19,419,625 58,258,876 29,129,438 14,564,719 43,694,158 21,847,079 65,541,238 32,770,619 98,311,858 49,155,929 147,467,788 73,733,894 36,866,947 110,600,842 55,300,421

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