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Old 2021-10-19, 00:28   #1
firejuggler
 
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"Vincent"
Apr 2010
Over the rainbow

1010011110102 Posts
Default birthday date, all format *2^n+1

24051981


Code:
24051981*2^24+1 (15 digits)
24051981*2^49+1 (23 digits)
24051981*2^53+1 (24 digits)
24051981*2^55+1 (24 digits)
24051981*2^71+1 (29 digits)
24051981*2^99+1 (38 digits)
24051981*2^104+1 (39 digits)
24051981*2^133+1 (48 digits)
24051981*2^144+1 (51 digits)
24051981*2^280+1 (92 digits)
24051981*2^323+1 (105 digits)
24051981*2^336+1 (109 digits)
24051981*2^435+1 (139 digits)
24051981*2^724+1 (226 digits)
24051981*2^1381+1 (424 digits)
24051981*2^2003+1 (611 digits)
24051981*2^2248+1 (685 digits)
24051981*2^2344+1 (713 digits)
24051981*2^2895+1 (879 digits)
24051981*2^3460+1 (1049 digits)
24051981*2^3913+1 (1186 digits)
24051981*2^5879+1 (1778 digits)
24051981*2^7393+1 (2233 digits)
24051981*2^8801+1 (2657 digits)
24051981*2^10837+1 (3270 digits)
24051981*2^11605+1 (3501 digits)
24051981*2^12496+1 (3770 digits)
24051981*2^12985+1 (3917 digits)
24051981*2^22380+1 (6745 digits)
24051981*2^28043+1 (8450 digits)
24051981*2^32917+1
24051981*2^36895+1
24051981*2^46464+1
24051981*2^53425+1
24051981*2^60953+1
24051981*2^95923+1
24051981*2^124421+1
24051981*2^226056+1
24051981*2^233387+1
19810524 (well technically 4952631 but you know...)

Code:
19810524*2^38+1
19810524*2^46+1
19810524*2^47+1
19810524*2^53+1
19810524*2^67+1
19810524*2^83+1
19810524*2^101+1
19810524*2^259+1
19810524*2^281+1
19810524*2^1085+1
19810524*2^1586+1
19810524*2^2405+1
19810524*2^2867+1
19810524*2^2918+1
19810524*2^2933+1
19810524*2^3479+1
19810524*2^4379+1
19810524*2^4823+1
19810524*2^5470+1
19810524*2^6125+1
19810524*2^7349+1
19810524*2^10159+1
19810524*2^10786+1
19810524*2^12065+1
19810524*2^20830+1
19810524*2^27110+1
19810524*2^55985+1
19810524*2^134999+1
19810524*2^169943+1
5241981


Code:
5241981*2^21+1
5241981*2^29+1
5241981*2^35+1
5241981*2^45+1
5241981*2^80+1
5241981*2^1119+1
5241981*2^1188+1
5241981*2^1268+1
5241981*2^1373+1
5241981*2^3288+1
5241981*2^3429+1
5241981*2^4035+1
5241981*2^5189+1
5241981*2^5700+1
5241981*2^12680+1
5241981*2^25260+1
5241981*2^37989+1

Last fiddled with by firejuggler on 2021-10-19 at 01:23
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Old 2021-10-19, 04:58   #2
kar_bon
 
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Mar 2006
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Please give search ranges for the n-values done.
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Old 2021-10-19, 12:02   #3
firejuggler
 
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Apr 2010
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i'm not done, of course, but I intend to fgo to 1e6
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Old 2021-10-19, 13:18   #4
Dr Sardonicus
 
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Feb 2017
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You did say, all format.

So, I entered the date May 24, 1981 AD (Gregorian calendar) into a Julian Day calculator.

Modified Julian Day 44,748 November 17. 1858 AD
Julian Day 2,444,748.5 noon on January 1. 4713 BC

I wasn't sure about the rounding, so...

44747*2^3 + 1
44747*2^131 + 1

44748*2^4 + 1
44748*2^8 + 1
44748*2^20 + 1
44748*2^24 + 1
44748*2^33 + 1
44748*2^48 + 1
44748*2^49 + 1
44748*2^60 + 1

44749*2^10 + 1
44749*2^46 + 1
44749*2^118 + 1
44749*2^186 + 1

2444747*2^7 + 1
2444747*2^75 + 1
2444747*2^119 + 1
2444747*2^127 + 1

2444748*2^1 + 1
2444748*2^4 + 1
2444748*2^40 + 1
2444748*2^52 + 1
2444748*2^100 + 1
2444748*2^124 + 1
2444748*2^154 + 1
2444748*2^192 + 1

2444749*2^2 + 1
2444749*2^194 + 1
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Old 2021-10-19, 15:49   #5
firejuggler
 
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Apr 2010
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did you check if they were gfn?
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Old 2021-10-20, 12:38   #6
Dr Sardonicus
 
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Quote:
Originally Posted by firejuggler View Post
did you check if they were gfn?
I'm not certain of what you mean by "gfn," but in any case the answer is no.
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Old 2021-10-20, 12:48   #7
kruoli
 
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GFN means most likely Generalized Fermat Numbers in this context.
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Old 2021-10-20, 13:12   #8
Dr Sardonicus
 
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Quote:
Originally Posted by kruoli View Post
GFN means most likely Generalized Fermat Numbers in this context.
That was the only "gfn" I could come up with that fit the context, but I wasn't certain that that was it.

One type of GFN is a^(2k) + 1, which none of the examples in this thread appear to be.

Another type of GFN is a^(2k) + b^(2k). I didn't check whether any examples in this thread are of that type.

All I checked was that the examples I posted had not tested composite with a BPSW test.
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Old 2021-10-20, 14:04   #9
kar_bon
 
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None of your given small primes are a divisor of any Generalized Fermat number.

Last fiddled with by kar_bon on 2021-10-20 at 14:05
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Old 2021-10-20, 15:10   #10
rogue
 
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Apr 2003
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What date formats? I can think of these (and there are likely more):

yyyymmdd (my personal favorite as it cannot easily be read incorrectly)
mmddyyyy (format popular in the US)
ddmmyyyy (format popular outside of the US)
yyyyjjj (jjj is the Julian day of the year)

And for those who don't care about the century:

yymmdd
mmddyy
ddmmyy
yyjjj

Last fiddled with by rogue on 2021-10-20 at 15:11
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Old 2021-10-20, 17:11   #11
firejuggler
 
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I will contend with the first three for now.
iso 8601 format , european format and USA format.


also http://www.fermatsearch.org/news.html

Last fiddled with by firejuggler on 2021-10-20 at 17:13
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