List of proposals for prime Argam numerals

Icarine-canonical prime Argam numerals are all based on the chemical elements — for instance, the ismarragam "sode" for digit-thirty-one (the eleventh prime number) derives from sodium, the eleventh element on the periodic table, as prime numbers can be seen as the "building blocks" of positive integers. However, this scheme only offers prime numerals up to the number of discovered elements, which there will be no canonical numeral for the primes beyond and any daughter numerals.

See a list of the first 118 prime numerals (2 through 647) here.

This page lists out known variants of the extended Argam numeral set. Due to the defining principles of the Argam numeral set, the proposals below are expected not to be Icarine-canon.

## Extended Periodic Table Variants

### Base-encoded IUPAC variants

These variants allow prime symbols and ismarragam to be generated systematically without any sort of chauvinism, however they are base-specific and in that aspect does not completely fit in the rationale of the numeral set.

#### Decimal IUPAC Variant

This variant's prime numbers are named after Decimal IUPAC names. For example, the 119th prime number will be based on the temporary IUPAC element name and symbol for element 119 "ununennium" (Uue).

#### Dozenal IUPAC Variant

Similar to the Decimal IUPAC Variant, this variant's prime numbers are named after Dozenal IUPAC names. Note that some IUPAC names will clash with current element symbols (ex. Element ten dozen seven "dekaseptium" with symbol Ds - That will clash with darmstadtium (Element 110) Those prime numbers may be given an arbitrary symbol. It generates prime symbols and ismarragam systematically without any sort of chauvinism, however they are base-specific and in that aspect does not completely fit in the rationale of the numeral set.

### Dozenalism's Priprefix Variant

This variant's prime numbers are simply named after the smaller Argam numerals. Ismarragam of those numbers are based on a combination of "pri-" from *prime* and the ismarragam of the prime index. One way to generate symbols is to utilize the remaining letter combinations that resemble the ismarragam of the prime index — for example, the next prime after oke (Decimal 647) is temporarily named "prisevote" and will represent digit-653, which could be represented with the stacked letters "Sv" from the prime index *sevote* (digit-119).

If another part were to go after "pri + N", the connector "sna" (derived from jan Misali's base nomenclature) is used as a "right bracket" to the "pri" prefix to indicate which part is supposed to be applied to prime(x), since prime(ab) does not equal to prime(a) times b.

* 426,409 = 6532 = prisevote-sna-ent → prisevote**sn**ent, as "prisevotent" could be interpreted as prime(sevotent)
* 430,327 = 653 × 659 = prisevote-prihund → prisevote**sna**prihund

Please note that the above proposal is non Valerian-canon and are only used as placeholder names for prime numbers that are yet to be named.

### ThatGuy30722's Bijective Hexavigesimal Variant

This variant utilizes the remaining letter combinations not assigned to the existing elements. 653, being the 119th prime, is written as a stacked "do", as 119 in bijective base 26 is , which using letters would be the fourth letter and the fifteenth letter, DO. So the primes go:

*Lv, Ts, Og, Do, Dp, Dq, Dr...*

For the next prime number, 677, we run into a problem: Ds is already used for an existing element, darmstadtium, and therefore is already used for digit-601. So, we look at what 601 WOULD have been, and use it for 677. 601 is the 110th prime, 110 in bijective hexavigesimal is DF, and since that's not used, 677 would be a stacked "df". Essentially Ds and Df switch places. So we keep going:

*Lv, Ts, Og, Do, Dp, Dq, Dr, Df, Dt, Du, Dv, Dw, Dx, Bn, Dz, Ea, Eb, Ec...*

Note that Dy (dysprosium, 317) has been switched with Bn, as 317 is the 66th (BN in bijective base 26) prime. Should a 119th element be named in the future, as say, Nw, then we would switch Do and Nw: 653 becomes Nw, and 2,671 (the original holder of Nw) would become Do.

Sometimes the switching gets really complicated: for example, 2,467 would be Na, but Na is already sodium, since sodium is the 11th element it would have been K, but that's taken by potassium which is 19th so it would be S, which is taken by sulfur which is 16th so it would be P, which is taken by phosphorus which is 15th so it would be O, which is taken by oxygen which is 8th so it would be H, which is taken by hydrogen which is 1st so it would be A, which isn't taken. So, after this long, unnecessarily complicated chain, we get to 2,467 being a stylized A. Another downside of the system is that every letter combination is possible (after Zz we do Aaa, Aab etc), so some really big primes would spell obscene words!

I don't remember how exactly the names were, I think I just used arbitrary names that sound like they could be abbreviated as those letters, so Dp could be called "dap" or something.

## Mixed Radix variants

### Decker Variant

This variant's larger primes and their multiples are based on its sexagesimal expansion. These numbers are represented by stacking two smaller argam, similar to the "chemical element" primes, like this:

n

m

{\displaystyle {\begin{matrix}n\\m\end{matrix}}}

. Where

n

{\displaystyle n}

 and

m

{\displaystyle m}

 represent the shocks (sixties) place and the ones place when expressed in base 60. For base 5,040,

n

{\displaystyle n}

 could go up to digit-eighty-three. This variant appears in De Vlieger's sketchbook, for kinsevoctoval (base 2,520) and sevoctovesimal (base 5,040). The base that the numerals are encoded in can be in other bases when seen fit, though the convention of using sexagesimal derives from that its base, sixty is superior highly composite and works well with numbers this size, and is considered optimal for encoding kinsevoctal and sevoctovesimal digits.

## Additive Definition Variants

### Alithian Variant

For prime numbers in this variant, simply add "un-" in front of the previous number. For instance, Digit-653 is the smallest prime that cannot be based on a discovered chemical element, therefore, the name should be based on the previous number, digit-652 "castron", so digit-653 would be "uncastron". So, digit-1,306, the double of digit-653 would be "diuncastron", and digit-1523 would be "undiunkinoctax" (un-di-un-kin-oct-ax), from

1
[
2
⋅
(
1
5
⋅

2

3

⋅
19
)
]

{\displaystyle 1+[2\cdot (1+5\cdot 2^{3}\cdot 19)]}

, since

1
5
⋅

2

3

⋅
# 19
761

{\displaystyle 1+5\cdot 2^{3}\cdot 19=761}

, which is prime. Numerals for this variant are currently undecided.

Like the Priprefix variant above, the connector "sna" is used.

* 426,409 = 6532 = uncastron-sna-ent → uncastron**sn**ent
* 430,327 = 653 × 659 = uncastron-unzeffoss → uncastron**sna**unzeffoss

Sub-variants of this system:

* "hen" could be used to replace "un" as the prefix for adding one.
* A prefix that doubles the number and adds one could be used, as all primes are one more than an even number.

### JiaGbon’s Sherlian Cipher

This proposal utilizes the methods of generating cipher text.

First, two-letter abbreviations will be generated for each argam numeral, which do not necessarily need to be unique. If the number is a compound (meaning having more than one root word), take the first two root words and take the first consonant in each of them, or else, take the first two letters of the ismarragam. For example, "kinsevoctove" (digit-2,520) is "ks" from the first two root words "kin" and "sev", and "erb" (digit-337) is "er".

As all primes >2 are odd, they can be expressed as the sum of two consecutive integers. (

# n
α
β

{\displaystyle n=\alpha+\beta}

 where

# α

n
−
1

2

{\displaystyle \alpha=\frac{n-1}{2}}

 and

# β

n
1

2

{\displaystyle \beta=\frac{n+1}{2}}

.) The two-letter abbreviations for the two ismarragam (

α

{\displaystyle \alpha}

 and

β

{\displaystyle \beta}

) will be put in a 2 by 2 matrix

[

α
1

α
2

β
1

β
2

]

{\displaystyle \begin{bmatrix} \alpha\_1 & \alpha\_2 \\ \beta\_1 & \beta\_2 \end{bmatrix}}

 where

α
1

{\displaystyle \alpha\_1}

 is the first letter of the two-letter abbreviation for

α

{\displaystyle \alpha}

,

α
2

{\displaystyle \alpha\_2}

 is the second letter and so on.

The letters will then be converted into a number from 1 through 26 depending on their position in the English alphabet (A=1, B=2 and so on). For each column, the sum of the two converted letters modulo 26 will then be converted back to a single letter. The two new letters obtained is the code for the prime and will be used to generate the ismarragam.

For example, the next three prime numbers would give:

# * 653
326
327
→

d
\_

i

s
\_

t
r
o
n

t
\_

r
i

c
\_

u
p
e

→

[

d

s

t

c

]

→

[

4

19

20

3

]

→

4
20

≡

24

(
mod

26
)

19
3

≡

22

(
mod

26
)

→

x

v

{\displaystyle 653=326+327\rightarrow \mathrm {{\underline {d}}i{\underline {s}}tron} +\mathrm {{\underline {t}}ri{\underline {c}}upe} \rightarrow {\begin{bmatrix}\mathrm {d} &\mathrm {s} \\\mathrm {t} &\mathrm {c} \end{bmatrix}}\rightarrow {\begin{bmatrix}4&19\\20&3\end{bmatrix}}\rightarrow {\begin{array}{lcl}4+20&\equiv &24{\pmod {26}}\\19+3&\equiv &22{\pmod {26}}\end{array}}\rightarrow {\begin{matrix}\mathrm {x} \\\mathrm {v} \end{matrix}}}
# * 659
329
330
→

s
\_

e

f
\_

o
s
s

k
\_

i
n
e

x
\_

e
l
l

→

[

s

f

k

x

]

→

[

19

6

11

24

]

→

19
11

≡

4

(
mod

26
)

6
24

≡

4

(
mod

26
)

→

d

d

{\displaystyle 659=329+330\rightarrow \mathrm {{\underline {s}}e{\underline {f}}oss} +\mathrm {{\underline {k}}ine{\underline {x}}ell} \rightarrow {\begin{bmatrix}\mathrm {s} &\mathrm {f} \\\mathrm {k} &\mathrm {x} \end{bmatrix}}\rightarrow {\begin{bmatrix}19&6\\11&24\end{bmatrix}}\rightarrow {\begin{array}{lcl}19+11&\equiv &4{\pmod {26}}\\6+24&\equiv &4{\pmod {26}}\end{array}}\rightarrow {\begin{matrix}\mathrm {d} \\\mathrm {d} \end{matrix}}}
# * 661
330
331
→

k
\_

i
n
e

x
\_

e
l
l

h
o

\_

l
m
e

→

[

k

x

h

o

]

→

[

11

24

8

15

]

→

11
8

≡

19

(
mod

26
)

24
15

≡

13

(
mod

26
)

→

s

m

{\displaystyle 661=330+331\rightarrow \mathrm {{\underline {k}}ine{\underline {x}}ell} +\mathrm {{\underline {ho}}lme} \rightarrow {\begin{bmatrix}\mathrm {k} &\mathrm {x} \\\mathrm {h} &\mathrm {o} \end{bmatrix}}\rightarrow {\begin{bmatrix}11&24\\8&15\end{bmatrix}}\rightarrow {\begin{array}{lcl}11+8&\equiv &19{\pmod {26}}\\24+15&\equiv &13{\pmod {26}}\end{array}}\rightarrow {\begin{matrix}\mathrm {s} \\\mathrm {m} \end{matrix}}}

.

The ismarragam for the numeral the derives from the two letters in the code.

If there is at least one vowel amongst the pair of letters in the prime, then combine the letters together. For example, the combination OB would give "ob". If both of the letters of the prime are consonants, then add an arbitrary vowel in-between both consonants that will not conflict with existing ismarragam or English word (Fx would give "fex", as fax, fix and fox are existing English words and "fux" may be confused with an obscene word). If both of the letters of the prime are vowels, a consonant is added instead. Other letters could be added at the end of the ismarragam when seem fit. In the case of the symbol being modified due to conflicts with smaller primes, the ismarragam will still derive from the numeral, and will be modified or weathered if necessary or seem fit (For instance, digit-661 will still be based on the Sm letter combination)

If the result is an English word or existing ismarragam for another numeral, then add arbitrary letters at the end of the two name parts. However, a silent e is often added at the end of the root word even if there are no conflicts.

Several letters are modified before the ismarragam is generated:

* "Ch-" and "Qu-" are used for the first letters C and Q respectively.
* A hard C can be used for the first letter K, and a soft C can be used for the first letter S, but using K and S is also acceptable.
* "-ce", "-ch", "-que", "sh" are used for the second letters C, H, Q and S respectively.
* For the second letter K, "-ck" and "-ke" are both acceptable.
* Sometimes, "th" is used in place of "t"
* A double L is sometimes used in place of a single L at the end of the ismarragam.

Finally, a two-letter symbol for the prime is generated from the ismarragam in the same way element symbols are generated.

## Variants with irregular patterns

### "Fanmade Chemical Elements" variant

This variant names prime numbers arbitrarily after famous scientists, mathematicians and philosophers, following the pattern of naming elements with atomic number 96 and above after scientists and places that have made a significant contribution to the scientific field of nuclear physics. The proposal was seen on the former "EX515 wiki" (which is now closed) which had pages that displayed numerals and ismarragam up to approximately 1,300 (ismarragam up to approximately 6,000 could be found in the source code of a template used on the wiki). It is believed that the numerals seen on the EX515 wiki were based on the fanmade elements found on "Fandomium". The "Paul Marciano Wiki" also includes similar work and uses the same assets used in the EX515 wiki.

It is the earliest known proposal for transelemental prime numerals. The numerals were produced and published years before the development of Valerian forms.

### Dozenalism's Valerian-canonical Variant

> *Main article: Valerian Argam Extension and Variants*
>
>

The numerals started off as an extension to the fanmade elements as described above as the original work only covers numerals up to digit-1,300. Through experimenting with different numberforms and ismarrgam, most of those numerals were eventually discarded and replaced by numerals with symbol and ismarrgam based on the properties of the prime number itself, or the prime index. The new numerals were mostly inspired by the prefix proposal as seen in "Day Gravity Water Spreadsheet" forum on DozensOnline.

Most of digits from 1,260 through 2,520 are named between 2020 and 2021 (with several small changes afterwards) after people Dozenalism met in his personal life as a way of expressing graditude and as a constant reminder of those who has made a positive impact in his life.

Pages about Argam numerals

## External Links

"Argam to Infinity / Expansions" on DozensOnline

## References

1. ↑ http://vincico.com/arqam/digits/argam-project.html