Problems & Puzzles: Puzzles

Puzzle 955. Variation of Puzzle 954

Now let's try the following variation of the puzzle 954:

Here we deal now with sequence of primes that grow for the center, two digits xy at a time, 00<=xy<=99, allowing repeated xy values.

According to the Giovanni's experience with the previous puzzle we should expect here non-exhaustive searches, so we must receive next Saturday only non-definitive results, unless...

An example, provided by Dmitry Kamenetsky:

677742876782841853126761781560842835690335834068580953966704099029404574518744251662080
231
529868962487611391669017016111556486507526243378211663016911550381434563500556643396
202585
374784544744516461 (198 digits)

Q1. Do you think that there is a largest solution or the sequence can be indefinitely large?

Q2. In any case, send your largest solution.

 

Contributions came from Seth Troisi, Giovanni Resta, Paul Cleary

Seth wrote on may 27, 2019

200 digits:

9999889889397875693938828310111675430578933140043151961573189349041480
48158076923828881975
75438631466544336992843965677101070200923453739572
871892099051805298367
850972747881560171732730690392204089307

***

Giovanni wrote on May 31, 2019

210 digits

1999798978876499669315424676860939579767373651336842427934858667010368
4550384034144684419098510119275248079524299077159363892347672729699260
0361292369215925733228015003695985393307691222736302678390789562559193

***

Paul wrote on May 31, 2019

Q1.  I donít think that there will be an indefinitely large solution and doubt it will be much larger than the 198 digits provided by Dmitry.

 

Q2.  The best I can do for now is a prime with 180 digits.

 

1153244899549650540677760463451999984709198611408030152000848785587578

4803685549461651846995300632720177896047155232769694335209216726543496

3562979391213089968734201198964228200781

***

 


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