Puzzle 1240 09/27/2025
Past Saturday, 09/27/2025, was a very special day
because this day, written in the USA date-format
(mm/dd/yyyy) and rewritten in the Europe & América
Latina date-format (dd/mm/yyyy), 27/09/2025 provides
integers that are perfect squares:
Usa Format: 09272025 = 3045^2
Europe & América Latina format: 27092025 =
5205^2
Q1.
Are other dates with the same property?
Q2. Are there dates in any (if both, the
better!) of the two formats, that are prefect
prime
squares (0001<yyyy<9999)?
Note: Please
never discard leading
zeros.
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From Oct 4 to 10, 2025, contributions came from Michael Branicky, Giorgos
Kalogeropoulos, Jeff Heleen, Gennady Gusev, Emmanuel Vantieghem,
***
Michael wrote:
I found the special day this year and 34 other such dates (Q1),
with those that are the squares of primes marked (Q2).
01010025 = 1005^2, 01010025 = 1005^2 04040100 = 2010^2, 04040100 = 2010^2
01030225 = 1015^2, 03010225 = 1735^2 03010225 = 1735^2, 01030225 = 1015^2
09090225 = 3015^2, 09090225 = 3015^2 07070281 = 2659^2, 07070281 = 2659^2
(US, EU-LA prime) 04120900 = 2030^2, 12040900 = 3470^2 12040900 = 3470^2,
04120900 = 2030^2 03031081 = 1741^2, 03031081 = 1741^2 (US, EU-LA prime)
06061444 = 2462^2, 06061444 = 2462^2 09272025 = 3045^2, 27092025 = 5205^2
01012036 = 1006^2, 01012036 = 1006^2 02022084 = 1422^2, 02022084 = 1422^2
08082649 = 2843^2, 08082649 = 2843^2 (US, EU-LA prime) 04223025 = 2055^2,
22043025 = 4695^2 05053504 = 2248^2, 05053504 = 2248^2 01014049 = 1007^2,
01014049 = 1007^2 04044121 = 2011^2, 04044121 = 2011^2 (US, EU-LA prime)
12124324 = 3482^2, 12124324 = 3482^2 03034564 = 1742^2, 03034564 = 1742^2
02024929 = 1423^2, 02024929 = 1423^2 (US, EU-LA prime) 11115556 = 3334^2,
11115556 = 3334^2 07075600 = 2660^2, 07075600 = 2660^2 01155625 = 1075^2,
15015625 = 3875^2 03316041 = 1821^2, 31036041 = 5571^2 10106041 = 3179^2,
10106041 = 3179^2 01016064 = 1008^2, 01016064 = 1008^2 09096256 = 3016^2,
09096256 = 3016^2 06066369 = 2463^2, 06066369 = 2463^2 02027776 = 1424^2,
02027776 = 1424^2 05058001 = 2249^2, 05058001 = 2249^2 03038049 = 1743^2,
03038049 = 1743^2 01018081 = 1009^2, 01018081 = 1009^2 (US, EU-LA prime)
04048144 = 2012^2, 04048144 = 2012^2 08088336 = 2844^2, 08088336 = 2844^2
***
Giorgos wrote:
01/01/0025 --> 01/01/0025 1005 -> False 1005 -> False
04/04/0100 --> 04/04/0100 2010 -> False 2010 -> False
01/03/0225 --> 03/01/0225 1015 -> False 1735 -> False
03/01/0225 --> 01/03/0225 1735 -> False 1015 -> False
09/09/0225 --> 09/09/0225 3015 -> False 3015 -> False
07/07/0281 --> 07/07/0281 2659 -> True 2659 -> True
04/12/0900 --> 12/04/0900 2030 -> False 3470 -> False
12/04/0900 --> 04/12/0900 3470 -> False 2030 -> False
03/03/1081 --> 03/03/1081 1741 -> True 1741 -> True
06/06/1444 --> 06/06/1444 2462 -> False 2462 -> False
09/27/2025 --> 27/09/2025 3045 -> False 5205 -> False
01/01/2036 --> 01/01/2036 1006 -> False 1006 -> False
02/02/2084 --> 02/02/2084 1422 -> False 1422 -> False
08/08/2649 --> 08/08/2649 2843 -> True 2843 -> True
04/22/3025 --> 22/04/3025 2055 -> False 4695 -> False
05/05/3504 --> 05/05/3504 2248 -> False 2248 -> False
01/01/4049 --> 01/01/4049 1007 -> False 1007 -> False
04/04/4121 --> 04/04/4121 2011 -> True 2011 -> True
12/12/4324 --> 12/12/4324 3482 -> False 3482 -> False
03/03/4564 --> 03/03/4564 1742 -> False 1742 -> False
02/02/4929 --> 02/02/4929 1423 -> True 1423 -> True
11/11/5556 --> 11/11/5556 3334 -> False 3334 -> False
07/07/5600 --> 07/07/5600 2660 -> False 2660 -> False
01/15/5625 --> 15/01/5625 1075 -> False 3875 -> False
03/31/6041 --> 31/03/6041 1821 -> False 5571 -> False
10/10/6041 --> 10/10/6041 3179 -> False 3179 -> False
01/01/6064 --> 01/01/6064 1008 -> False 1008 -> False
09/09/6256 --> 09/09/6256 3016 -> False 3016 -> False
06/06/6369 --> 06/06/6369 2463 -> False 2463 -> False
02/02/7776 --> 02/02/7776 1424 -> False 1424 -> False
05/05/8001 --> 05/05/8001 2249 -> False 2249 -> False
03/03/8049 --> 03/03/8049 1743 -> False 1743 -> False
01/01/8081 --> 01/01/8081 1009 -> True 1009 -> True
04/04/8144 --> 04/04/8144 2012 -> False 2012 -> False
08/08/8336 --> 08/08/8336 2844 -> False 2844 -> False
***
Jeff wrote:
For Q1 I found 822 dates in USA format. Smallest = 01010025 = 1005^2.
Largest = 12313081 = 3509^2>
In EU & Latina format I found 571 dates. Smallest = 01010025 = 1005^2.
Largest = 31125241 = 5579^2.
For Q2 there are 114 dates in USA format. Smallest = 01018081 = 1009^2.
Largest = 12243001 = 3499^2.
In EU & Latina format I found 90 dates. Smallest = 01018081 = 1009^2.
Largest = 31058329 = 5573^2.
There are many instances where the same date in both formats works,
There are also instances where different dates produce the same number.
Eg, Jan 10, 4601 and Oct 1, 4601 each give 01104601 in both formats.
The next date for USA prime is Feb 4, 2041 -> 02042041 = 1429^2.
The
next date for EU/Latina prime is Apr 2, 2041 -> 02042041 = 1429^2.
***
Gennady wrote:
Q1.
Only 6 dates written in both formats in different ways are perfect
squares.
(mm/dd/yyyy) (dd/mm/yyyy)
"01030225" -> 1015, "03010225" -> 1735
"01155625" -> 1075, "15015625" -> 3875
"03316041" -> 1821, "31036041" -> 5571
"04120900" -> 2030, "12040900" -> 3470
"04223025" -> 2055, "22043025" -> 4695
"09272025" -> 3045, "27092025" -> 5205
The remaining 27 are written the same way.
Q2. Only dates written in both formats in the same way are perfect
squares of the prime numbers.
"01018081" -> 1009
"02024929" -> 1423
"03031081" -> 1741
"04044121" -> 2011
"07070281" -> 2659
"08082649" -> 2843
***
Emmanuel wrote:
I
found 33 days with the same property :
(I mention the E-LA notation first if it differs from the other)
01010025 = 1005^2
04040100 = 2010^2
03010225 = 1735^2 ; 01030225 = 1015^2
09090225 = 3015^2
07070281 = 2659^2 (prime squared)
12040900 = 3470^2 ; 04120900 = 2030^2
03031081 = 1741^2 (prime squared)
06061444 = 2462^2 ; 6061444 = 2462^2
27092025 = 5205^2 ; 09272025 = 3045^2 (found already)
01012036 = 1006^2
02022084 = 1422^2
08082649 = 2843^2 (prime squared)
22043025 = 4695^2 ; 04223025 = 2055^2
05053504 = 2248^2
01014049 = 1007^2
04044121 = 2011^2 (prime squared)
12124324 = 3482^2
03034564 = 1742^2
02024929 = 1423^2 (prime squared)
11115556 = 3334^2
07075600 = 2660^2
15015625 = 3875^2 ; 1155625 = 1075^2
31036041 = 5571^2 ; 3316041 = 1821^2
10106041 = 3179^2
01016064 = 1008^2
09096256 = 3016^2
06066369 = 2463^2
02027776 = 1424^2
05058001 = 2249^2
03038049 = 1743^2
01018081 = 1009^2 (prime squared)
04048144 = 2012^2
08088336 = 2844^2
Q2
There are 90 days that are squares of primes on the E-LA notation :
25030009,25090081,12020089,25110121,26020201,07070281,23030401,01100401,13010449,02070721,05031049,
03031081,15031129,02111209,26081449,07091569,17081689,28121809,04012009,03052009,02042041,17032129,
15062161,11082241,11042329,01042441,10042561,08082649,13082689,01062961,03073009,05013121,19123129,
30063289,02053489,
31013761,13053769,,02093809,12033961,16024009,03094081,04044121,16104169,15124321,09114361,29084449,
01104601,02024929,02105401,11095561,01125721,06115729,11015761,19035769,08025889,16056049,06086089,
09066121,13126129,01026169,02036329,06046681,04116841,05067001,01067089,21077281,20097289,18088009,
01018081,
08128201,28058209,22118209,24098281,04068289,31058329,01038361,08048569,17048641,02128681,04108729,
10118761,20079361,24039409,30019441,01079521,23049601,07059649,29019769,10029889,01129969,
There are 114 days that are squares of primes on the USA notation :
12020089,01190281,07070281,05230369,01100401,03200521,02070721,07230721,04280761,05031049,03031081,
01261129,02211169,02111209,01181569,07091569,03052009,04012009,02042041,11082241,07252249,11042329,
11202409,01042441,08162449,10182481,10042561,08082649,01142761,11282881,01062961,05202961,12243001,
03073009,02283121,
05013121,02193361,03193369,09223369,01203409,02053489,03243601,02093809,02163841,12033961,03094081,
04044121,07134241,09114361,01104601,07284601,01274641,01194649,04214809,02024929,06265009,08185321,
02105401,06135529,11095561,11175649,01125721,06115729,11015761,08025889,04255969,06086089,09066121,
01026169,05276209,
11296321,02036329,07166329,09296401,05166529,01216609,06046681,04116841,10156969,02247001,05067001,
12187081,01067089,02217121,04157521,09247681,10297681,01247689,03157729,05257849,01018081,08128201,
04068289,01038361,05148361,07198489,09138529,08048569,08288641,02128681,04108729,10118761,02229049,
03179089,10259209
02199289,05139289,01079521,07059649,03279721,01229881,10029889,01129969,07219969
Those that are squares of primes are mentioned in the first table.
***
