Palindromic dates in the YYYYMMDD format

Today, 20211202 (2nd December 2021), is a palindrome in the YYYYMMDD format. It is the 83rd of what will ultimately be 366 palindromic dates in this format.

  • The first of these was 01011010 (10th October 101).
  • The most recent one was 20200202 (2nd February 2020).
  • The next one is 20300302 (2nd March 2030).
  • The last one will be 92900929 (29th September 9290).

Dates of this format come in waves separated by huge gaps. There were no palindromic dates of this format between 13800831 (31st August 1380) and 20011002 (2nd October 2001). Between 2001 and 22900922 (22nd September 2290), we can expect about one every ten years. Then a similarly huge gap appears until 30011003 (3rd October 3001). This repeating millennium-long pattern, of a few centuries of about one per decade followed by many more centuries of nothing, has been visible since the epoch, and will continue fairly regularly until the year number hits five digits.

(For the record, the best date format is not YYYYMMDD but YYYY-MM-DD, which is always totally unambiguous and allows lexicographical sorting. Dates in this format are never palindromic, due to the placement of the hyphens.)

Full list

Every possible birthday appears in this listing exactly once! To figure out yours,

  • take your birthday, say 16th February
  • express it in MMDD format: 0216
  • add four digits on the front to turn that into a palindrome: 61200216
  • look for 61200216 (16th February 6120) in the table.
#YYYYMMDDDDs MMMM YYYYDays until next
10101101010th October 1013014
20110011010th January 110669
30111111010th November 1113014
40120021010th February 120669
50121121010th December 1213012
60130031010th March 1303684
70140041010th April 1403682
80150051010th May 1503684
90160061010th June 1603682
100170071010th July 1703684
110180081010th August 1803683
120190091010th September 1904057
130201102020th October 2013014
140210012020th January 210669
150211112020th November 2113014
160220022020th February 220669
170221122020th December 2213012
180230032020th March 2303684
190240042020th April 2403682
200250052020th May 2503684
210260062020th June 2603682
220270072020th July 2703684
230280082020th August 2803683
240290092020th September 2904057
250301103030th October 3013014
260310013030th January 310669
270311113030th November 3113683
280321123030th December 3213012
290330033030th March 3303684
300340043030th April 3403682
310350053030th May 3503684
320360063030th June 3603682
330370073030th July 3703684
340380083030th August 3803683
350390093030th September 390223164
36100110011st October 10013014
37101001011st January 1010669
38101111011st November 10113014
39102002011st February 1020669
40102112011st December 10213012
41103003011st March 10303684
42104004011st April 10403682
43105005011st May 10503684
44106006011st June 10603682
45107007011st July 10703684
46108008011st August 10803683
47109009011st September 10904057
481101101111th October 11013014
491110011111th January 1110669
501111111111th November 11113014
511120021111th February 1120669
521121121111th December 11213012
531130031111th March 11303684
541140041111th April 11403682
551150051111th May 11503684
561160061111th June 11603682
571170071111th July 11703684
581180081111th August 11803683
591190091111th September 11904058
601201102121st October 12013014
611210012121st January 1210669
621211112121st November 12113014
631220022121st February 1220669
641221122121st December 12213012
651230032121st March 12303684
661240042121st April 12403682
671250052121st May 12503684
681260062121st June 12603682
691270072121st July 12703684
701280082121st August 12803683
711290092121st September 12904057
721301103131st October 13013014
731310013131st January 13104352
741321123131st December 13213012
751330033131st March 13307366
761350053131st May 13507366
771370073131st July 13703684
781380083131st August 1380226847
79200110022nd October 20013014
80201001022nd January 2010669
81201111022nd November 20113014
82202002022nd February 2020669
83202112022nd December 20213012
84203003022nd March 20303684
85204004022nd April 20403682
86205005022nd May 20503684
87206006022nd June 20603682
88207007022nd July 20703684
89208008022nd August 20803683
90209009022nd September 20904057
912101101212th October 21013014
922110011212th January 2110669
932111111212th November 21113014
942120021212th February 2120669
952121121212th December 21213012
962130031212th March 21303684
972140041212th April 21403682
982150051212th May 21503684
992160061212th June 21603682
1002170071212th July 21703684
1012180081212th August 21803683
1022190091212th September 21904057
1032201102222nd October 22013014
1042210012222nd January 2210669
1052211112222nd November 22113014
1062220022222nd February 2220669
1072221122222nd December 22213012
1082230032222nd March 22303684
1092240042222nd April 22403682
1102250052222nd May 22503684
1112260062222nd June 22603682
1122270072222nd July 22703684
1132280082222nd August 22803683
1142290092222nd September 2290259698
115300110033rd October 30013014
116301001033rd January 3010669
117301111033rd November 30113014
118302002033rd February 3020669
119302112033rd December 30213012
120303003033rd March 30303684
121304004033rd April 30403682
122305005033rd May 30503684
123306006033rd June 30603682
124307007033rd July 30703684
125308008033rd August 30803683
126309009033rd September 30904057
1273101101313th October 31013014
1283110011313th January 3110669
1293111111313th November 31113014
1303120021313th February 3120669
1313121121313th December 31213012
1323130031313th March 31303684
1333140041313th April 31403682
1343150051313th May 31503684
1353160061313th June 31603682
1363170071313th July 31703684
1373180081313th August 31803683
1383190091313th September 31904058
1393201102323rd October 32013014
1403210012323rd January 3210669
1413211112323rd November 32113014
1423220022323rd February 3220669
1433221122323rd December 32213012
1443230032323rd March 32303684
1453240042323rd April 32403682
1463250052323rd May 32503684
1473260062323rd June 32603682
1483270072323rd July 32703684
1493280082323rd August 32803683
1503290092323rd September 3290259698
151400110044th October 40013014
152401001044th January 4010669
153401111044th November 40113014
154402002044th February 4020669
155402112044th December 40213012
156403003044th March 40303684
157404004044th April 40403682
158405005044th May 40503684
159406006044th June 40603682
160407007044th July 40703684
161408008044th August 40803683
162409009044th September 40904057
1634101101414th October 41013014
1644110011414th January 4110669
1654111111414th November 41113014
1664120021414th February 4120669
1674121121414th December 41213012
1684130031414th March 41303684
1694140041414th April 41403682
1704150051414th May 41503684
1714160061414th June 41603682
1724170071414th July 41703684
1734180081414th August 41803683
1744190091414th September 41904057
1754201102424th October 42013014
1764210012424th January 4210669
1774211112424th November 42113014
1784220022424th February 4220669
1794221122424th December 42213012
1804230032424th March 42303684
1814240042424th April 42403682
1824250052424th May 42503684
1834260062424th June 42603682
1844270072424th July 42703684
1854280082424th August 42803683
1864290092424th September 4290259698
187500110055th October 50013014
188501001055th January 5010669
189501111055th November 50113014
190502002055th February 5020669
191502112055th December 50213012
192503003055th March 50303684
193504004055th April 50403682
194505005055th May 50503684
195506006055th June 50603682
196507007055th July 50703684
197508008055th August 50803683
198509009055th September 50904057
1995101101515th October 51013014
2005110011515th January 5110669
2015111111515th November 51113014
2025120021515th February 5120669
2035121121515th December 51213012
2045130031515th March 51303684
2055140041515th April 51403682
2065150051515th May 51503684
2075160061515th June 51603682
2085170071515th July 51703684
2095180081515th August 51803683
2105190091515th September 51904058
2115201102525th October 52013014
2125210012525th January 5210669
2135211112525th November 52113014
2145220022525th February 5220669
2155221122525th December 52213012
2165230032525th March 52303684
2175240042525th April 52403682
2185250052525th May 52503684
2195260062525th June 52603682
2205270072525th July 52703684
2215280082525th August 52803683
2225290092525th September 5290259698
223600110066th October 60013014
224601001066th January 6010669
225601111066th November 60113014
226602002066th February 6020669
227602112066th December 60213012
228603003066th March 60303684
229604004066th April 60403682
230605005066th May 60503684
231606006066th June 60603682
232607007066th July 60703684
233608008066th August 60803683
234609009066th September 60904057
2356101101616th October 61013014
2366110011616th January 6110669
2376111111616th November 61113014
2386120021616th February 6120669
2396121121616th December 61213012
2406130031616th March 61303684
2416140041616th April 61403682
2426150051616th May 61503684
2436160061616th June 61603682
2446170071616th July 61703684
2456180081616th August 61803683
2466190091616th September 61904057
2476201102626th October 62013014
2486210012626th January 6210669
2496211112626th November 62113014
2506220022626th February 6220669
2516221122626th December 62213012
2526230032626th March 62303684
2536240042626th April 62403682
2546250052626th May 62503684
2556260062626th June 62603682
2566270072626th July 62703684
2576280082626th August 62803683
2586290092626th September 6290259698
259700110077th October 70013014
260701001077th January 7010669
261701111077th November 70113014
262702002077th February 7020669
263702112077th December 70213012
264703003077th March 70303684
265704004077th April 70403682
266705005077th May 70503684
267706006077th June 70603682
268707007077th July 70703684
269708008077th August 70803683
270709009077th September 70904057
2717101101717th October 71013014
2727110011717th January 7110669
2737111111717th November 71113014
2747120021717th February 7120669
2757121121717th December 71213012
2767130031717th March 71303684
2777140041717th April 71403682
2787150051717th May 71503684
2797160061717th June 71603682
2807170071717th July 71703684
2817180081717th August 71803683
2827190091717th September 71904058
2837201102727th October 72013014
2847210012727th January 7210669
2857211112727th November 72113014
2867220022727th February 7220669
2877221122727th December 72213012
2887230032727th March 72303684
2897240042727th April 72403682
2907250052727th May 72503684
2917260062727th June 72603682
2927270072727th July 72703684
2937280082727th August 72803683
2947290092727th September 7290259698
295800110088th October 80013014
296801001088th January 8010669
297801111088th November 80113014
298802002088th February 8020669
299802112088th December 80213012
300803003088th March 80303684
301804004088th April 80403682
302805005088th May 80503684
303806006088th June 80603682
304807007088th July 80703684
305808008088th August 80803683
306809009088th September 80904057
3078101101818th October 81013014
3088110011818th January 8110669
3098111111818th November 81113014
3108120021818th February 8120669
3118121121818th December 81213012
3128130031818th March 81303684
3138140041818th April 81403682
3148150051818th May 81503684
3158160061818th June 81603682
3168170071818th July 81703684
3178180081818th August 81803683
3188190091818th September 81904057
3198201102828th October 82013014
3208210012828th January 8210669
3218211112828th November 82113014
3228220022828th February 8220669
3238221122828th December 82213012
3248230032828th March 82303684
3258240042828th April 82403682
3268250052828th May 82503684
3278260062828th June 82603682
3288270072828th July 82703684
3298280082828th August 82803683
3308290092828th September 8290259698
331900110099th October 90013014
332901001099th January 9010669
333901111099th November 90113014
334902002099th February 9020669
335902112099th December 90213012
336903003099th March 90303684
337904004099th April 90403682
338905005099th May 90503684
339906006099th June 90603682
340907007099th July 90703684
341908008099th August 90803683
342909009099th September 90904057
3439101101919th October 91013014
3449110011919th January 9110669
3459111111919th November 91113014
3469120021919th February 9120669
3479121121919th December 91213012
3489130031919th March 91303684
3499140041919th April 91403682
3509150051919th May 91503684
3519160061919th June 91603682
3529170071919th July 91703684
3539180081919th August 91803683
3549190091919th September 91904058
3559201102929th October 92013014
3569210012929th January 9210669
3579211112929th November 92113014
3589220022929th February 9220669
3599221122929th December 92213012
3609230032929th March 92303684
3619240042929th April 92403682
3629250052929th May 92503684
3639260062929th June 92603682
3649270072929th July 92703684
3659280082929th August 92803683
3669290092929th September 9290

Intervals

Intervals between one palindromic date and the next show some repetition. Here is how frequently different intervals appear:

Interval (days)Count
66959
301231
301460
368260
368331
368491
405716
40585
43521
73662
2231641
2268471
2596987
Total365

Discussion (16)

2021-12-02 00:45:09 by qntm:

See you all in nine-and-a-bit years.

2021-12-02 06:48:31 by hobbs:

And sometimes (well, twice a century in the centuries that have palindromes at all), a gap of one year and ten months works, incrementing both of the middle digits.

2021-12-02 18:04:37 by laverya:

The prevalence of 669 is interesting - almost 20% of 'days until next' is that number.

2021-12-02 18:23:38 by SubmanUK:

Another great post from DataGenetics! … wait where am i? :)

2021-12-02 21:32:23 by Boter:

New life goal: live life long enough to reach my birthday palindrome.

2021-12-02 21:45:22 by P:

Less than 300 years till my birthday is a palindrome! Guess I'm one of the lucky ones.

2021-12-03 05:31:36 by tanamr:

Can't wait til we get to the palindromic year 19391 (which is also 1969)

2021-12-08 18:33:56 by mszegedy:

Despite the following table of interval counts, it took me a while to understand what the "days until next" column was for. If anyone else is wondering: it's the length of the interval between that row's palindromic date and the next row's, in days. (Before that, my best guess was the interval between 2021 Dec 2 and that date, which was obviously nonsense, and caused me great confusion.

2021-12-08 18:34:17 by mszegedy:

)

2021-12-17 07:38:37 by Ingvar:

Well, both YYYYMMDD and YYYY-MM-DD sort lexicographically (the "-" does not influence the ordering, as all YYYY-MM-DD dates will have the "-" in the same place). But, yes, given a choice between YYYYMMDD and YYYY-MM-DD, I will choose the latter every time. But if the choice is between MM/DD/YYYY or YYYY/DD/MM and YYYYMMDD, I will pick YYYYMMDD without a second's hesitation. I would also posit that it is allowable to ignore the separators when judging for palindromeness (and, likewise, capitalisation), otherwise "A man, a plan, a canal, Panama!" would not be a palindrome and it is pretty much the epitome of standard examples of one in the English language. But, yeah, somewhat harder to write a palindrome checker for.

2022-01-14 02:01:13 by wroughage:

Is there significance to the total being 365? Kind of a weird total. (I know it's 365+ d/y)

2022-01-14 02:03:18 by qntm:

Yes, for each of the 366 possible days in the year there is a palindromic date, and between the 366 palindromic dates there are 365 intervals.

2022-01-21 17:06:47 by MrRandom:

Interesting to see.

2022-01-22 04:58:09 by David:

This is great. Thank you!

2022-03-23 01:53:24 by Soyfish:

That's really cool

2022-05-09 15:35:37 by iewqr:

qntm,I love your creations! From this article,scp antimeme division to hatetris.Keep the good work!

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