List all Right Truncatable Primes. A Right Truncatable Prime is a prime number which contains no 0 and if the rightmost digit is successively removed, then all resulting numbers are primes. For example, 7193 – since 7193, 719, 71 and 7 all are primes.
📌 Challenge Details and Links
ExcelBI Excel Challenge Number: 286
Challenge Difficulty: ⭐️⭐️
📥Download Sample File
📥Link to the solutions on LinkedIn
Solving the challenge of List all Right Truncatable Primes with Power Query
Power Query solution 1 for List all Right Truncatable Primes, proposed by Zoran Milokanović:
let
Source = Excel.CurrentWorkbook(){[Name = "Input"]}[Content][Numbers],
IsPrime = (n) =>
not List.Accumulate(
{2 .. Number.RoundDown(Number.Sqrt(n))},
n = 1,
(s, d) => s or (Number.Mod(n, d) = 0)
),
S = List.Select(
Source,
each
let
t = Text.From(_)
in
List.Accumulate(
{1 .. Text.Length(t)},
true,
(s, d) => s and IsPrime(Number.From(Text.Start(t, d)))
)
)
in
SPower Query solution 2 for List all Right Truncatable Primes, proposed by Alejandro Simón 🇵🇦 🇪🇸:
let
Source = Excel.CurrentWorkbook(){[Name = "Table1"]}[Content],
Sol = Table.SelectRows(
Source,
each
let
a = Text.From([Numbers]),
b = Text.Length(a),
c = List.Transform(
{1 .. b},
each
let
d = Number.From(Text.Range(a, 0, _)),
e = List.Transform(
{2} & List.Select({3 .. Int64.From(Number.Sqrt(d))}, Number.IsOdd),
(x) => Number.Mod(d, x) <> 0
)
in
List.AllTrue(e)
)
in
List.AllTrue(c)
)
in
SolPower Query solution 3 for List all Right Truncatable Primes, proposed by Luan Rodrigues:
let
Fonte = Tabela1,
fx = (n) =>
List.Select({2 .. Number.RoundDown(Number.Sqrt(n))}, (x) => Number.Mod(n, x) = 0){0}? = null,
fil = Table.SelectRows(
Fonte,
each [
a = List.Select(
{2 .. Number.RoundDown(Number.Sqrt([Numbers]))},
(x) => Number.Mod([Numbers], x) = 0
){0}?
= null,
b = Text.From([Numbers]),
c = List.Select(
List.Transform({0 .. Text.Length(b)}, each Number.From(Text.Middle(b, 0, _))),
each _ <> null
),
d = List.AllTrue(List.Transform(c, (x) => fx(x))) = true,
e = a = true and d = true
][e]
)
in
filPower Query solution 4 for List all Right Truncatable Primes, proposed by Rafael González B.:
let
Source = Excel.CurrentWorkbook(){0}[Content],
TC = Table.TransformColumnTypes(Source, {{"Numbers", type number}}),
Fx_Prime = (n as number) =>
let
a = n,
b = Text.From(a),
c = Text.ToList(b),
d = List.Count(c),
e = d - 1,
ee =
let
ee1 = List.FirstN(c, e),
ee2 = Text.Combine(ee1),
ee3 = Number.From(ee2)
in
ee3,
f = {2 .. Number.RoundDown(Number.Sqrt(a))},
g = Table.FromList(f, Splitter.SplitByNothing(), {"Divisors"}),
h = Table.AddColumn(g, "Num", each Number.Mod(a, [Divisors])),
i = Table.SelectRows(h, each [Num] = 0),
j = Table.IsEmpty(i),
k = if not j then "No" else if ee = null then "Yes" else @Fx_Prime(ee)
in
k,
Col = Table.AddColumn(TC, "Check", each Fx_Prime([Numbers])),
Result = Table.SelectRows(Col, each ([Check] = "Yes"))[[Numbers]]
in
ResultPower Query solution 5 for List all Right Truncatable Primes, proposed by Luke Jarych:
let
Source = Table1,
ConvertToText = Table.TransformColumnTypes(Source, {{"Numbers", type text}}), // Convert "Numbers" back to number
IsAllPrime = Table.AddColumn(ConvertToText, "AllDigitsPrime", each IsAllPrime([Numbers])),
#"Filtered Rows" = Table.SelectRows(IsAllPrime, each ([AllDigitsPrime] = true)),
#"Removed Columns" = Table.RemoveColumns(#"Filtered Rows",{"AllDigitsPrime"})
in
#"Removed Columns"
IsPrime = let
IsPrime = (num as number) as logical =>
let
maxDivisor = Number.RoundDown(Number.Sqrt(num)),
divisible = List.Numbers(2, maxDivisor - 1),
checkDivisible = List.Select(divisible, each Number.Mod(num, _) = 0)
in
List.IsEmpty(checkDivisible) and num >= 1
in IsPrime
IsAllPrime =
let CheckRightTruncatablePrime = (numText as text) as logical =>
let
num = Number.From(numText),
numLength = Text.Length(numText),
truncatedPrime = Number.RoundDown(num / 10),
isCurrentPrime = IsPrime(num),
isNextPrime = if numLength > 1 then IsAllPrime(Text.Start(Text.From(truncatedPrime), numLength - 1)) else true
in
isCurrentPrime and isNextPrime
in
CheckRightTruncatablePrime
Solving the challenge of List all Right Truncatable Primes with Excel
Excel solution 1 for List all Right Truncatable Primes, proposed by John V.:
=TOCOL(
MAP(
A2:A11,
LAMBDA(
n,
n/AND(
MAP(
INT(
n/10^SEQUENCE(
LEN(
n
),
,
0
)
),
LAMBDA(
x,
AND(
MOD(
x,
1+SEQUENCE(
x^0.5
)
)
)
)
)
)
)
),
2
)Excel solution 2 for List all Right Truncatable Primes, proposed by محمد حلمي:
=TOCOL(
MAP(
A2:A11,
LAMBDA(
a,
a/AND(
MAP(
9-SEQUENCE(
8
),
LAMBDA(
d,
AND(
MOD(
LEFT(
a,
d
)/SEQUENCE(
LEFT(
a,
d
)^0.5,
,
2
),
1
)
)
)
)
)
)
),
2
)
=TOCOL(
MAP(
A2:A11,
LAMBDA(
a,
a/REDUCE(
1,
9-SEQUENCE(
8
),
LAMBDA(
c,
d,
AND(
VSTACK(
c,
MOD(
LEFT(
a,
d
)/SEQUENCE(
LEFT(
a,
d
)^0.5,
,
2
),
1
)
)
)
)
)
)
),
2
)Excel solution 3 for List all Right Truncatable Primes, proposed by Kris Jaganah:
=TOCOL(MAP(A2:A11,
LAMBDA(x,
LET(a,
--MID(
x,
1,
SEQUENCE(
LEN(
x
)
)
),
b,
(a+1)/6,
c,
(a-1)/6,
x/MIN(IFS(a=2,
1,
a=3,
1,
a=5,
1,
1,
(INT(
b
)=b)+(INT(
c
)=c)))))),
3)Excel solution 4 for List all Right Truncatable Primes, proposed by Timothée BLIOT:
=FILTER(A2:A11,MAP(A2:A11,LAMBDA(z,LET(D,LAMBDA(n,IF(n<5,2,VSTACK(2,SEQUENCE(ROUNDDOWN(((n^0.5)-3),0)/2+1,,3,2)))),P,LAMBDA(x, SWITCH(x,1,0,2,1,LET(A,D(x),--(SUM(MAP(A, LAMBDA(a,--(MOD(x,a)=0)))) =0)))),A,MAP(SEQUENCE(LEN(z),,LEN(z),-1),LAMBDA(x,P(MID(z,1,x)*1))),IF(--RIGHT(z)>0,SUM(A)=ROWS(A))))))Excel solution 5 for List all Right Truncatable Primes, proposed by Hussein SATOUR:
=FILTER(
A2:A11,
MAP(
A2:A11,
LAMBDA(
x,
MIN(
MAP(
--UNIQUE(
MID(
x,
1,
SEQUENCE(
9
)
)
),
LAMBDA(
y,
MIN(
DROP(
MOD(
y,
SEQUENCE(
ROUNDUP(
SQRT(
y
),
0
)
)
),
1
)
)
)
)
)
)
)<>0
)Excel solution 6 for List all Right Truncatable Primes, proposed by Sunny Baggu:
=TOCOL(
A2:A11 * 1 /
MAP(
A2:A11,
LAMBDA(num,
AND(
MAP(
LEFT(num, SEQUENCE(LEN(num))) + 0,
LAMBDA(x,
IF(x <= 3, "TRUE", OR(BYCOL((x + {1, -1}) / 6, LAMBDA(a, a = INT(a)))))
)
)
)
)
),
3
)Excel solution 7 for List all Right Truncatable Primes, proposed by LEONARD OCHEA 🇷🇴:
=TOCOL(MAP(A2:A11,
LAMBDA(n,
LET(e,
INT(
n*10^-SEQUENCE(
LEN(
n
),
,
0
)
),
n/AND(MAP(e,
LAMBDA(a,
LET(x,
(a+1)/6,
y,
(a-1)/6,
OR(
a=3,
a=2,
x=INT(
x
),
y=INT(
y
)
)))))))),
3)Excel solution 8 for List all Right Truncatable Primes, proposed by Charles Roldan:
=LET(
B, LAMBDA(f, LAMBDA(g, LAMBDA(x, f(g(x))))),
M, LAMBDA(f, LAMBDA(x, MAP(x, f))),
F, LAMBDA(f, LAMBDA(x, FILTER(x, M(f)(x)))),
All, B(F)(B(LAMBDA(x, AND(x)))),
Primes, B(M(LAMBDA(n, IFERROR(AND(MOD(n, DROP(SEQUENCE(SQRT(n)), 1))), n > 1)))),
Pieces, LAMBDA(n, --LEFT(n, SEQUENCE(LEN(n)))),
All(Primes(Pieces))
)(A2:A11)Excel solution 9 for List all Right Truncatable Primes, proposed by Julien Lacaze:
=LET(
data,
A2:A10,
isPrime,
LAMBDA(
value,
SUM(
N(
MOD(
value,
SEQUENCE(
SQRT(
value
)
)
)=0
)
)=1
),
isRightPrime,
LAMBDA(
n,
f,
IF(
LEN(
n
)=1,
isPrime(
n
),
f(
QUOTIENT(
n,
10
),
f
)
)
),
FILTER(
data,
MAP(
data,
LAMBDA(
d,
isRightPrime(
d,
isRightPrime
)
)
)
)
)Excel solution 10 for List all Right Truncatable Primes, proposed by Pieter de Bruijn:
=TOCOL(
MAP(
A2:A11,
LAMBDA(
a,
a/AND(
MAP(
LEN(
a
)-SEQUENCE(
LEN(
a
)-1
),
LAMBDA(
d,
AND(
ISERROR(
FIND(
0,
a
)
),
MOD(
LEFT(
a,
d
)/SEQUENCE(
LEFT(
a,
d
)^0.5,
,
2
),
1
)
)
)
)
)
)
),
2
)
or since any number containing a 0 will have a number ending with -0 between the checks for primes,
the multiple of 10 will be divisable (by at least 2 and 5 (and 10)),
therefore we can skip the ISERROR(
FIND(
0,
a
)
) part:
=TOCOL(
MAP(
A2:A11,
LAMBDA(
a,
a/AND(
MAP(
LEN(
a
)-SEQUENCE(
LEN(
a
)-1
),
LAMBDA(
d,
AND(
MOD(
LEFT(
a,
d
)/SEQUENCE(
LEFT(
a,
d
)^0.5,
,
2
),
1
)
)
)
)
)
)
),
2
)Excel solution 11 for List all Right Truncatable Primes, proposed by Giorgi Goderdzishvili:
=LAMBDA(x,MAP(x,
LAMBDA(y,
IF(OR(y=2,y=3,y=1),1,IF(SUM(--(MOD(y,SEQUENCE(INT(y^0.5)-3,,3,1))=0))>0,0,1)))))
Solution:
=TOCOL(MAP(A2:A11,LAMBDA(x,LET(
nm,x,
sq,SUM( IFERROR(isPrime(--MID(nm,1,SEQUENCE(,LEN(nm),LEN(nm),-1))),1)),
nm/(sq=LEN(nm))))),3)Excel solution 12 for List all Right Truncatable Primes, proposed by Abdelrahman Omer, MBA, PMP:
=TOCOL(MAP(A2:A11,LAMBDA(a,LET(b,M&ID(a,1,SEQUENCE(LEN(a),,LEN(a),-1)),c,(MID(a,SEQUENCE(LEN(a)),1)+0<>0),d,IF(b=2,TRUE,IF(AND(MOD(b,ROW(INDIRECT("2:"&ROUNDUP(SQRT(b),0))))<>0),TRUE,FALSE)),e,SUM(c*d),FILTER(a,e>0)))),3)Excel solution 13 for List all Right Truncatable Primes, proposed by Daniel Garzia:
=TOCOL(
MAP(
A2:A11,
LAMBDA(
x,
x/AND(
MAP(
0+LEFT(
x,
SEQUENCE(
LEN(
x
),
,
LEN(
x
),
-1
)
),
LAMBDA(
r,
AND(
ISERR(
FIND(
0,
r
)
),
MOD(
r,
SEQUENCE(
ROUNDUP(
r^0.5,
)-1,
,
2
)
)
)
)
)
)
)
),
2
)Excel solution 14 for List all Right Truncatable Primes, proposed by samir tobeil:
=1,
SUM(--(MOD(
x,
SEQUENCE(
9
)
)=0))=1),
--CONCAT(
FIND(
MID(
x,
ROW(
1:20
),
1
),
"13579"
)
),
"a")))))Excel solution 15 for List all Right Truncatable Primes, proposed by Jeff Blakley:
=LET(isPrime,
LAMBDA(num,
IFS(num<10,
OR(
num={2,
3,
5,
7}
),
OR(
MOD(
num,
2
)=0,
MOD(
num,
3
)=0
),
FALSE,
1,
SUM(--MAP(SEQUENCE(ROUNDUP((INT(
SQRT(
num
)
)-4)/6,
0),
,
5,
6),
LAMBDA(
i,
OR(
MOD(
num,
i
)=0,
MOD(
num,
i+2
)=0
)
)))=0)),
criteria,
MAP(
A2:A11,
LAMBDA(
x,
SUM(
--MAP(
--LEFT(
x,
SEQUENCE(
LEN(
x
)
)
),
LAMBDA(
y,
NOT(
isPrime(
y
)
)
)
)
)=0
)
),
FILTER(
A2:A11,
criteria
))Solving the challenge of List all Right Truncatable Primes with Python
Python solution 1 for List all Right Truncatable Primes, proposed by Alejandro Simón 🇵🇦 🇪🇸:
Show translation
Solving the challenge of List all Right Truncatable Primes with Python in Excel
Python in Excel solution 1 for List all Right Truncatable Primes, proposed by John V.:
Hi everyone!
One (Python) option could be:
Blessings!
Python in Excel solution 2 for List all Right Truncatable Primes, proposed by JvdV -:
With PY():
from sympy import *
list(filter(lambda n:all([isprime(int(str(n)[:x+1])) for x in range(len(str(n)))]), xl("A2:A11")[0]))Solving the challenge of List all Right Truncatable Primes with R
R solution 1 for List all Right Truncatable Primes, proposed by Konrad Gryczan, PhD:
library(tidyverse)
library(readxl)
input = read_excel("Right Truncatable Primes.xlsx") %>% select(1)
is_prime <- function(n) {
if (n <= 1) {
return(FALSE)
}
if (n <= 3) {
return(TRUE)
}
if (n %% 2 == 0 || n %% 3 == 0) {
return(FALSE)
}
i <- 5
while (i * i <= n) {
if (n %% i == 0 || n %% (i + 2) == 0) {
return(FALSE)
}
i <- i + 6
}
return(TRUE)
}
is_right_truncatable_prime <- function(n) {
while (n > 0) {
if (!is_prime(n)) {
return(FALSE)
}
n <- n %/% 10
}
return(TRUE)
}
result = input %>%
mutate(is_rtp = map_lgl(Numbers, is_right_truncatable_prime)) %>%
filter(is_rtp == TRUE) %>%
select(Numbers)
&&