perfect numbers comparison on my writings

The 6, 28, 496, 8028 and 33, 550, 336 are the first few perfect numbers.

The thing about perfect numbers is that, above 6, they all divide by four from 28 to infinity.

They are all divide by 4 (28 and up), by 6 (496 and bigger), by 7 with 28 and internally above 28 , and by 8 (496 and up).

The internal mod 7, (multiples of seven) in perfect numbers starting with 28, is that all perfect number to infinity are even, and, except 28, (4×7) are internally an odd or even multiple of 7, plus 1, if the multiple of 7 is odd(example: 33,550,335 +1), or plus 6, if the multiple of seven is even.

Examples:

496 is 490, an even multiple of 7, +6.

490 even is 7×70.

8028 is 8022 (an even multiple of 7) +6.

8022 even is 7000+700+280+42.

33,550,335 is an odd multiple of 7, which added to 1, because two odds make an even, forces the perfect number 33,550,336 to be even.

33,550,335(an odd mult of 7)+1 = the perfect number 33,550,336.

33,550,33[5] is 28m+4.9m+630k+14k+6335.

All perfect numbers including 6 are triangular because tetrahedrons are triangular.

They form triangles and tetrahedrons to infinity.

Tetrahedrons pack tightly into clusters of 20, which clusters are called icosahedrons, which also pack tightly. There is no room for odd perfect numbers.

Perfect numbers can literally be represented as triangles and/or tetrahedrons.

Perfect numbers can also be represented as squares and cubes.

Like with triangles and tetrahedrons, you can substitute each integer with one square or cube.

The number 6, which is 6 integers (6 ones), can be represented by 6 triangles, one 4-sided tetrahedron and 2 triangles, or 6 tetrahedrons.

Alternately, the 6 can, likewise, be represented by 6 squares, or one, 6-sided cube, or 6 cubes.

Not only do perfect numbers stack and cluster, they ring too, whether in 2-D triangle or square rings or 3-D rings of cubes.

Cubes cluster into larger cube clusters, which make a shell that encloses each shell starting with the center cube.

The first shell is 26 cubes, which encloses the center cube; making a perfect 27 cube cluster, which is three layers of 9 cubes.

27 is not a perfect number.

One more cube makes the perfect # 28.

The second shell is 98 cubes, which encloses the 27 cube cluster. The total of the bigger cluster is 125 (98+27),which is 5 layers of 25 cubes(5×5×5). The next cluster is 7×7×7(7×49), which is 343. The next shell bigger than 98 cubes is 343-98, which is 245 cubes. The shell encloses the inner cubes.

The next perfect number is 496. 496-300=196-43=153.

153 can be one, 125-cube cluster (5×25 cubes), plus one 27-cube cluster (3×9 cubes), plus 1 cube.

The 343 cube cluster, plus the other clusters of 125 and 27, and the remaining single leftover cube make the perfect number 496.

This clustering and cubing goes to infinity and the tetrahedron making goes to infinity, with zero fragments. These cube clusters 27, 125, 343 and cube shells, 26, 98, and 245 are not perfect numbers themselves, but they can fill up perfect numbers with cubes.

Perfect number in cubes leave cube remainders, but no fractional decimal fragments. They are whole cubes.

With tetrahedrons, perfect numbers divide with no decimal fragmentd, though there is a remainder of tetrahedrons when dividing off icosahedrons clusters of 20 tetrahedrons.

FibetyJibets, Aug. 9, 2026

Perfect numbers are exactly filled up, and filled in, by equal sized pyramidal tetrahedrons.

They pack tightly. Each tetrahedron is made of four equilateral triangles🔺. This exact filling of perfect numbers with pyramidal tetrahedrons scales to infinity.

A tetrahedron is [four] equilateral triangles🔺🔺🔺🔺 (of equal lines) folded concentrically together into a pyramidal tetrahedron.

The fact that perfect numbers divide by 4, again and again, until they come to four(4) equal Mersenne primes is no coincidence. Example: 496 ÷4 = 124. 124÷4= 31.

31 is a Mersenne prime.

24 icosahedrons, which are spherical clusters of 20 tetrahedrons, represent 480 tetrahedrons of 496 tetrahedrons. 16 more pyramidal tetrahedrons make the perfect number 496 with no dangling fraction or fragment.

Structurally, there can be no phantom odd perfect unless, you can make a 4 a 3, or a 3 into a 4, or a tetrahedron with 3 triangles instead of 4.

People speculate that there might be some astronomically big perfect number that could be odd because they see no geometrical structure filling them.

They seem mysterious and become astronomical in size as the base of a tetrahedron is larger than the apex tip.

Perfect numbers stack, tessellate, and ring as triangles and inverted triangles.

Perfect numbers as tetrahedrons cluster into icosahedrons.

This is hard to show here in text.

Try to picture upright and inverted triangles stacked or tessellated tightly as a grid of triangles.

__________∆

_______.∆∆∆∆

_____∆∆∆∆∆∆∆

Some see perfect numbers as triangular by looking at stacks of balls, but they are not as tightly packed as tetrahedrons clustered into icosahedrons.

There is internal structure in all perfect numbers forcing them to be even.

Internally, perfect numbers are all either an odd multiple of 7 plus 1, or and even multiple of 7 plus 6. Either way, this forces an even number.

Examples:

A) The "perfect" 496 is 490 +6.

490 is a multiple of 7 (7×70).

B) The "perfect" 8028 is 8022 +6.

8022 is a multiple of 7 (7000+700+280+42).

C) The "perfect" 33,550,336 is 33,550,335 +1.

33,550,335 is a multiple of 7 (28million+4.9m+630k+14k+6,300+35).

Perfect numbers ALL divide by four (4), and geometrically form an exactitude of tetrahedrons, which are four triangles each, except the starter 6, which can be viewed as either

6 triangles🔻🔺🔻🔺🔻🔺,

1 tetrahedron ∆ and two triangles🔻🔺,

(I could not find a tetrahedron emoji.)

or as 6 tetrahedrons ∆∆∆∆∆∆,

or as

6 squares⬜⬜⬜⬜⬜⬜,

1 cube📦, or

6 cubes📦📦📦📦📦📦.

Four(4) sided tetrahedrons exactly fill in all perfect numbers.

With any perfect number, you can substitute tetrahedrons for each integer.

For example: 496 tetrahedrons.

FibetyJibets, August 11, 2026

🥺😐🔺📦Perfect numbers are exactly filled up, and filled in, by equal sized pyramidal tetrahedrons.

They pack tightly. Each tetrahedron is made of four equilateral triangles🔺. This exact filling of perfect numbers with pyramidal tetrahedrons scales to infinity.

A tetrahedron is [four] equilateral triangles🔺🔺🔺🔺 (of equal lines) folded concentrically together into a pyramidal tetrahedron.

The fact that perfect numbers divide by 4, again and again, until they come to four(4) equal Mersenne primes is no coincidence. Example: 496 ÷4 = 124. 124÷4= 31.

31 is a Mersenne prime.

Structurally, there can be no phantom odd perfect unless, you can make a 4 a 3, or a 3 into a 4, or a tetrahedron with 3 triangles instead of 4.

People speculate that there might be some astronomically big perfect number that could be odd because they see no geometrical structure filling them.

They seem mysterious and become astronomical in size as the base of a tetrahedron is larger than the apex tip.

Perfect numbers stack, tessellate, and ring as triangles and inverted triangles.

Perfect numbers as tetrahedrons cluster into icosahedrons.

This is hard to show here in text.

Try to picture upright and inverted triangles stacked or tessellated tightly as a grid of triangles.

__________∆

_______.∆∆∆∆

_____∆∆∆∆∆∆∆

Some see perfect numbers as triangular by looking at stacks of balls, but they are not as tightly packed as tetrahedrons clustered into icosahedrons.

There is internal structure in all perfect numbers forcing them to be even.

Internally, perfect numbers are all either an odd multiple of 7 plus 1, or and even multiple of 7 plus 6. Either way, this forces an even number.

Examples:

A) The "perfect" 496 is 490 +6.

490 is a multiple of 7 (7×70).

B) The "perfect" 8028 is 8022 +6.

8022 is a multiple of 7 (7000+700+280+42).

C) The "perfect" 33,550,336 is 33,550,335 +1.

33,550,335 is a multiple of 7 (28million+4.9m+630k+14k+6,300+35).

Perfect numbers ALL divide by four (4), and geometrically form an exactitude of tetrahedrons, which are four triangles each, except the starter 6, which can be viewed as either

6 triangles🔻🔺🔻🔺🔻🔺,

1 tetrahedron ∆ and two triangles🔻🔺,

(I could not find a tetrahedron emoji.)

or as 6 tetrahedrons ∆∆∆∆∆∆,

or as

6 squares⬜⬜⬜⬜⬜⬜,

1 cube📦, or

6 cubes📦📦📦📦📦📦.

Four(4) sided tetrahedrons exactly fill in all perfect numbers.

With any perfect number, you can substitute tetrahedrons for each integer.

For example: 496 tetrahedrons.

FibetyJibets, August 11, 2026

😐*****The 6, 28, 496, 8028 and 33, 550, 336 are the first few perfect numbers.

The thing about perfect numbers is that, above 6, they all divide by four from 28 to infinity.

They all divide by 4 (28 and up), by 6 (496 and bigger), 28 by 7(28÷7=4), and internally above 28 , and by 8 (496 and up).

The internal mod 7, (multiples of seven) in perfect numbers is that all perfect numbers greater than 28, (4×7) are internally an odd or even multiple of 7, plus 1 or 6; if the internal multiple of 7 is odd then 1 more completes the perfect number (example: 33,550,335 +1), and if the internal multiple of seven is even, 6 completes the perfect.

Examples:

490, an even multiple of 7, +6 = 496

490 even is 7×70.

8022 (an even multiple of 7) +6= 8028

8022 even is 7000+700+280+42.

33,550,335 is an odd multiple of 7, which added to 1, because two odds make an even, forces the perfect number 33,550,336 to be even.

33,550,335(an odd mult of 7)+1 = the perfect number 33,550,336.

33,550,33[5] is 28m+4.9m+630k+14k+6335.

All perfect numbers including 6 are triangular because tetrahedrons and triangles fill them in tight packing, with no fragments of fractions, and tetrahedrons are triangular.

They form triangles and tetrahedrons to infinity.

Tetrahedrons pack tightly into clusters of 20, which clusters are icosahedrons, which also pack tightly. There is no logical geometric permission for odd perfect numbers. Mersenne primes stop perfects from being odd. Internally, they are tied to a system that forces perfect numbers to be even by combining odd and even multiples of 7 to a 1 or 6.