World!Of
Numbers  WON plate
224 |

[ May 20, 2023 ] [ Last update June 2, 2023 ]
Prepending n digits d to k so that [d^^n][k] becomes
a record delayed prime
Xinyao Chen (email)

While WONplate 197 is appending digits to the RIGHT of a number,
now let us consider prepending digits to the LEFT of the number.
Except for 0, all digits 1 to 9 can be used, but of course we only
consider the numbers k both coprime to 10 and coprime to d (since all
numbers [d^^n][k] are divisible by gcd(k,10) and gcd(k,d)).

Here are the record k-values for each case in base 10.

( '^^' is symbol for concatenation )

Also when numbers get larger I will accept PRP (PRobable Prime)
as valid entries.

Click on the header titles to open the related worksheets from Xinyao Chen.
The main page is at → https://sites.google.com/view/world-of-numbers-plate-219/

 BASE 10 Prime byprepending 1's Prime byprepending 2's Prime byprepending 3's [1^^1] [2^^3] [3^^1] [1^^17] [2^^204] [3^^2] [1^^713] [2^^19151] [3^^4] [1^^3372] [2^^30843] [3^^7] [1^^35793] [2^^34697] [3^^8] [1^^ >100000] [2^^ >100000] [3^^34] [3^^24037] [3^^ >100000]  to  by Xinyao Chen &  by PDG  to  by Xinyao Chen to  by PDG  to  by Xinyao Chen to  by PDG See alsoA200065 ```Sequence [k] in order of increasing prepended digits 1's. Each value < n in [d^^n][k] must be composite. ``` ```Sequence [k] in order of increasing prepended digits 2's. Each value < n in [d^^n][k] must be composite. ``` ```Sequence [k] in order of increasing prepended digits 3's. Each value < n in [d^^n][k] must be composite. ``` Prime byprepending 4's Prime byprepending 5's Prime byprepending 6's [4^^1] [5^^11] [6^^1] [4^^2] [5^^69] [6^^5037] [4^^15] [5^^182] [6^^ >100000] [4^^50] [5^^240] [4^^187] [5^^645] [4^^837] [5^^1683] [4^^2846] [5^^79773] [4^^3112] [5^^ >100000] [4^^9688] [4^^ >100000]  to  by Xinyao Chen & 1551 by PDG  to  by Xinyao Chen &  by PDG  to  by Xinyao Chen by PDG ```Sequence [k] in order of increasing prepended digits 4's. Each value < n in [d^^n][k] must be composite. ``` ```Sequence [k] in order of increasing prepended digits 5's. Each value < n in [d^^n][k] must be composite. ``` ```Sequence [k] in order of increasing prepended digits 6's. Each value < n in [d^^n][k] must be composite. ``` Prime byprepending 7's Prime byprepending 8's Prime byprepending 9's [7^^1] [8^^2] [9^^2] [7^^3] [8^^3] [9^^1798] [7^^18] [8^^77] [9^^3527] [7^^64] [8^^96] [9^^8654] [7^^173] [8^^11592] [9^^ >100000] [7^^2502] [8^^68805] [7^^21186] [8^^89100] [7^^ >100000] [8^^ >100000]  to  by Xinyao Chen &  by PDG  to  by Xinyao Chen to  by PDG  to  by Xinyao Chen &  by PDG ```Sequence [k] in order of increasing prepended digits 7's. Each value < n in [d^^n][k] must be composite. ``` ```Sequence [k] in order of increasing prepended digits 8's. Each value < n in [d^^n][k] must be composite. ``` ```Sequence [k] in order of increasing prepended digits 9's. Each value < n in [d^^n][k] must be composite. ``` ```
\\ This is the PARI/GP program code for WONplate 224 by PDG [June 2, 2023]
\\ ie. making sequence [k] in order of increasing prepended digits d's.
\\ Each value < n in [d^^n][k] must be composite.
{
d=7;
for(a=1, 100,
b=1;
until(flag==0,
f=(d*(10^a-1)/9)*10^(#(digits(b)))+b;
while(ispseudoprime(f)==0,
b+=2; f=(d*(10^a-1)/9)*10^(#(digits(b)))+b;
);
\\ print(f); print(a,"  ",b);
for(i=1, a-1,
if(ispseudoprime(fd), flag++; break(); );
);
b+=2;
);
print("[",d,"^^",a,"][",b-2,"]");
b=1;
)
}

``` A000224 Prime Curios! Prime Puzzle  Wikipedia 224 Le nombre 224 ```

```

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