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 231529868962487611391669017016111556486507526243378211663016911550381434563500556643396 202585374784544744516461 (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.

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Contributions came from Seth Troisi, Giovanni Resta, Paul Cleary

Seth wrote on may 27, 2019

200 digits:

9999889889397875693938828310111675430578933140043151961573189349041480
4815807692382888197575438631466544336992843965677101070200923453739572
871892099051805298367850972747881560171732730690392204089307

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Giovanni wrote on May 31, 2019

210 digits

1999798978876499669315424676860939579767373651336842427934858667010368
4550384034144684419098510119275248079524299077159363892347672729699260
0361292369215925733228015003695985393307691222736302678390789562559193

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Paul wrote on May 31, 2019

Q1.  I don’t 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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