Problems & Puzzles: Puzzles

Puzzle 457. Prime word embedded.

Rodolfo Kurchan sent the following nice puzzle:

Find the smallest prime number whose name written in English contains the letters "PRIME" in order embedded in it. 

Q1. Solve the Rodolfo question.
Q2. Redo it in your origin language.


Frederick Schneider wrote:

Q1. For American and Modern British English, the answer is:

1000000000000000035000061: one sePtillion thiRty-fIve Million sixty-onE

In the "Traditional British" and "Traditional European" numbering, the
first number containing a P is also sePtillion but sePtillion is
defined as 10^42 in these systems. The rest of the letters can be found in a similar way.

The smallest prime is 10^42 + 35000007: one sePtillion thiRty fIve
Million sEven.

Q2. Assuming you don't want to translate PRIME into another language,
for Indonesian, the answer is much smaller (perhaps the smallest?): 859 = delaPan-Ratus LIMa-puluh sEmbilan (eight hundred fifty-nine)

(What if we want to translate "Prime" to Indonesian?. Frederick responded: The original word for prime is "ganjil" but there's
no numbers in Indonesian that contain the letter g, so...)


Luke Pebody wrote:

Q1. Is it "one sePtillion thiRty-fIve Million sixty-onE?"

I am pretty sure that the P does not appear in anything below one
septillion, that the M can come from nothing smaller than a million,
and that thirty five is the smallest number to contain R and I in that
order. This shows a lower bound of one septillion and thirty five
million. The next prime above 10^24+35*10^6 is 10^24+35*10^6+61.

If you speak British, then a septillion is 10^42, so the answer is


Carlos Rivera wrote:

Q2. I found in Spanish "Prime" or "Primo" in the same smallest prime number: 10^42+30*10^3+21 = Septillón Treintamil Veintiuno


J. C. Rosa wrote:

About Q2 , in French : "PRIME"="PREMIER" , I found the following
result:  704003=sept cent quatre mille trois. I think that this prime number is the smallest in French.


Patrick Capelle wrote:

Q2, in French.

Word « PRIME »:
73009 = septante-trois mille neuf *
703013 = sept cent trois mille treize **

Word « PREMIER »:
74047 = septante-quatre mille quarante-sept *
704003 = sept cent quatre mille trois **

* Belgium, Suisse romande, Val d'Aoste, East of France, République démocratique du Congo, Rwanda.
** France


Nick McGrath wrote (Aug., 08):

Just for amusement I tried some other embedded names of numbers.
The smallest I could come up with were:

10^117 + 10^60 + 10^24 +16
= one oCtOtrigintillion one noveMdecillion one sePtilliOn SIxTEen

6*10^15 + 11*10^6 + 750*10^3 + 889
=Six QUAdRillion Eleven million seven hundred fifty thousand eight hundred eighty nine

oNe quAdrillion Twenty foUR thousAnd eLeven.



About the Nick's contribution my comment is this:

Find the smallest X-number such that when written in L-language the word X appears in order. X= Square, Triangular, Fibonacci, etc. (See Puzzle 459)



Rodolfo Kurchan wrote (Aug., 08):

Te mando las soluciones que recibí en Snark de Jaime Rudas de Bogotá:

Creo que encontré una solución para el número primo en alemán, con las letras en orden:

HAUPTZAHL (número primo)

HundertAchtUndzwanzig sePTillionen achtZigtAusendacHthunderteLf
128 x 10^42 + 80811

En Portugués:


um sePtilião e tRInta Mil centO e cinquenta e um

En Ruso:

531 163 - Пятьсот тРидцать Одна тыСяча сТО шЕстьдесят три
531 163 - Pyat'sot tRidtsat' Odna tySyacha sTO shEst'decyat' tri

En Holandés:

één sePtiljoen dRIE Miljoen honderdneGEnenTAchtigduizend achthonderdeLf
10^42 + 3 189 811


Gennady Gusev wrote (Set 08)

I would like to suppose my solutions of the puzzles 457 and 459 for Russian language.
In Russian there are no letters U (У) and F (Ф) in name of numbers so Natural, Fibonacci, Triangular and Factorial are impossible. The term 'OTHER' is not used.


Пять тысяч тРиста девянОСТО дЕвять
Pyat' tysyach tRista devyanOSTO dEvyat'

СОрок тыСяч ТристА деВяНОсто чЕтыре
SOrok tySyach Trista deVyaNOsto chEtyre

сороК миллионоВ тристА семьДесят тРи тысячи тристА шесТнадцать
soroK millionoV tristA sem'Desyat tRi tysyachi tristA shesTnadtsat'

сЕмьсОТ СОРок тысяч сто Пятьдесят три
sEm'sOT SORok tysyach sto Pyat'desyat tri


Claudio Meller wrote (March 2011):

Solutions in Spanish

Smaller number with the letters of Natural :
1.440.000 uN millón cuATrocientos cUaRentA miL

Smaller number with the letters of Cuadrado (square in spanish) :
4.231.249: CUAtro millones Doscientos tReintA y un mil DOscientos cuarenta y nueve

Smaller number with the letters of Square :
2514:  doS mil QUinientos cAtoRcE 

Smaller number with the letters of Emirp :
trEs MIl tRes sePtillones

Smaller number with the letters of Composite  :
CuatrO Mil sePtillones Ochenta y SIeTE

Smaller number with the letters of Compuesto (composite in spanish):
CuatrO Mil sePtillones cUatrociEntoS cuaTro




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