# Fibonacci-Primes

Here are the first 200 Fibonacci numbers, and the list below them shows you whether they are Prime (True) or not (False).

{1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, \

2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, \

317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, \

14930352, 24157817, 39088169, 63245986, 102334155, 165580141, \

267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, \

4807526976, 7778742049, 12586269025, 20365011074, 32951280099, \

53316291173, 86267571272, 139583862445, 225851433717, 365435296162, \

591286729879, 956722026041, 1548008755920, 2504730781961, \

4052739537881, 6557470319842, 10610209857723, 17167680177565, \

27777890035288, 44945570212853, 72723460248141, 117669030460994, \

190392490709135, 308061521170129, 498454011879264, 806515533049393, \

1304969544928657, 2111485077978050, 3416454622906707, \

5527939700884757, 8944394323791464, 14472334024676221, \

23416728348467685, 37889062373143906, 61305790721611591, \

99194853094755497, 160500643816367088, 259695496911122585, \

420196140727489673, 679891637638612258, 1100087778366101931, \

1779979416004714189, 2880067194370816120, 4660046610375530309, \

7540113804746346429, 12200160415121876738, 19740274219868223167, \

31940434634990099905, 51680708854858323072, 83621143489848422977, \

135301852344706746049, 218922995834555169026, 354224848179261915075, \

573147844013817084101, 927372692193078999176, 1500520536206896083277, \

2427893228399975082453, 3928413764606871165730, \

6356306993006846248183, 10284720757613717413913, \

16641027750620563662096, 26925748508234281076009, \

43566776258854844738105, 70492524767089125814114, \

114059301025943970552219, 184551825793033096366333, \

298611126818977066918552, 483162952612010163284885, \

781774079430987230203437, 1264937032042997393488322, \

2046711111473984623691759, 3311648143516982017180081, \

5358359254990966640871840, 8670007398507948658051921, \

14028366653498915298923761, 22698374052006863956975682, \

36726740705505779255899443, 59425114757512643212875125, \

96151855463018422468774568, 155576970220531065681649693, \

251728825683549488150424261, 407305795904080553832073954, \

659034621587630041982498215, 1066340417491710595814572169, \

1725375039079340637797070384, 2791715456571051233611642553, \

4517090495650391871408712937, 7308805952221443105020355490, \

11825896447871834976429068427, 19134702400093278081449423917, \

30960598847965113057878492344, 50095301248058391139327916261, \

81055900096023504197206408605, 131151201344081895336534324866, \

212207101440105399533740733471, 343358302784187294870275058337, \

555565404224292694404015791808, 898923707008479989274290850145, \

1454489111232772683678306641953, 2353412818241252672952597492098, \

3807901929474025356630904134051, 6161314747715278029583501626149, \

9969216677189303386214405760200, 16130531424904581415797907386349, \

26099748102093884802012313146549, 42230279526998466217810220532898, \

68330027629092351019822533679447, 110560307156090817237632754212345, \

178890334785183168257455287891792, 289450641941273985495088042104137, \

468340976726457153752543329995929, 757791618667731139247631372100066, \

1226132595394188293000174702095995, \

1983924214061919432247806074196061, \

3210056809456107725247980776292056, \

5193981023518027157495786850488117, \

8404037832974134882743767626780173, \

13598018856492162040239554477268290, \

22002056689466296922983322104048463, \

35600075545958458963222876581316753, \

57602132235424755886206198685365216, \

93202207781383214849429075266681969, \

150804340016807970735635273952047185, \

244006547798191185585064349218729154, \

394810887814999156320699623170776339, \

638817435613190341905763972389505493, \

1033628323428189498226463595560281832, \

1672445759041379840132227567949787325, \

2706074082469569338358691163510069157, \

4378519841510949178490918731459856482, \

7084593923980518516849609894969925639, \

11463113765491467695340528626429782121, \

18547707689471986212190138521399707760, \

30010821454963453907530667147829489881, \

48558529144435440119720805669229197641, \

78569350599398894027251472817058687522, \

127127879743834334146972278486287885163, \

205697230343233228174223751303346572685, \

332825110087067562321196029789634457848, \

538522340430300790495419781092981030533, \

871347450517368352816615810882615488381, \

1409869790947669143312035591975596518914, \

2281217241465037496128651402858212007295, \

3691087032412706639440686994833808526209, \

5972304273877744135569338397692020533504, \

9663391306290450775010025392525829059713, \

15635695580168194910579363790217849593217, \

25299086886458645685589389182743678652930, \

40934782466626840596168752972961528246147, \

66233869353085486281758142155705206899077, \

107168651819712326877926895128666735145224, \

173402521172797813159685037284371942044301, \

280571172992510140037611932413038677189525}

{False, False, True, True, True, False, True, False, False, False, \

True, False, True, False, False, False, True, False, False, False, \

False, False, True, False, False, False, False, False, True, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, True, False, False, False, True, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, True, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

True, False, False, False, False, False, True, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False, \

False, False, False, False, False, False, False, False, False, False}

# The Sunflower Seed-Head Yet Again

# Still Even More on the Golden Ratio

The well-known Fibonacci sequence formed by summing consecutive terms looks like:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89……….

And a well known property of this sequence is that if you take the ratio of consecutive terms you get closer and closer to the Golden Ratio the higher up the sequence you go. So if we divide 89 by 55 we get 1.61818181…….

We can create a Fibonacci series incorporating the variable x in the following way:

1, x, (1+x), (1+2x), (2+3x), (3+5x), (5+8x), (8+13x)…

Now a remarkable property of this sequence is that once again, if we take the ratio of consective terms in the sequence, we get the Golden Ratio – Phi – provided x=Phi, which I think is a remarkable result.

What this means is that looking at the sequence with Phi replacing x we get:

1, Phi, (1 + Phi), (1 + 2*Phi), (2 + 3*Phi), (3 + 5*Phi)…

And if taking the ratio of consective terms gives us Phi, this means that:

(1 + Phi) = Phi^2

(1 + 2*Phi) = Phi^3

(2 + 3*Phi) = Phi^4

The first result comes directly from the basic definition of Phi itself, namely that (1 + Phi)/Phi = Phi

Taking a deeper look at the above sequence I was able to come up with a general result, namely:

Phi^n + 2*Phi^(n+1) = Phi^(n+3)

# Comet Garradd in 3D

Here is a 3-D view of comet Garradd. You can view the stereograph by:

- Using the Cross-Eyed method.
- Using 3D prism glasses (berezin.com/3d/3dprism.htm)
- Using Brian May’s OWL Stereoscope (londonstereo.com)

I took the image of the comet using a Hyperstar III on a Celestron C11 SCT and an M25C OSC CCD camera from Starlight Xpress. The Dr. Brian May created the stereograph from the CCD image.

# Greg’s “3” Asterism in Leo – in 3D

Here is a 3-D view of Greg’s “3” asterism which can be found in the constellation Leo. You can view the stereograph by:

- Using the Cross-Eyed method.
- Using 3D prism glasses (berezin.com/3d/3dprism.htm)
- Using Brian May’s OWL Stereoscope (londonstereo.com)

I took the image of the asterism using the Sky90 refractors and the M26C OSC CCDs on the MiniWASP array at the New Forest Observatory. Dr. Brian May created the stereograph from my Deep-Sky image.

# Cabbage White Butterfly Eggs in 3D

Here is a 3-D view of the eggs of the Cabbage White butterfly. You can view the stereograph by:

- Using the Cross-Eyed method.
- Using 3D prism glasses (berezin.com/3d/3dprism.htm)
- Using Brian May’s OWL Stereoscope (londonstereo.com)

I took the images of the Cabbage White butterfly eggs using a Canon 5D MkII DSLR and a research trinocular microscope. The 2 images are focus-stacked using the Helicon Focus software, and Dr. Brian May created the stereograph.

# 3D VIEW OF DNA

Here is a 3-D view of 2 and a half periods of the DNA molecule. You can view the stereograph by:

- Using the Cross-Eyed method.
- Using 3D prism glasses (berezin.com/3d/3dprism.htm)
- Using Brian May’s OWL Stereoscope (londonstereo.com)

I put together the 3D model from a Cochrane’s of Oxford kit, and Dr. Brian May created the stereograph.

# 6-Minute Space Station Pass 02/12/2022

It’s been a loooong time since I’ve done one of these – so I’ve got a bit out of practice. But this was tonight’s Space Station pass at 5:37 p.m. I got part of a nice long 6-minute pass and you see it disappears off the top of the screen where there is the glow from a very bright Moon. I will do better next time

# Star reduced Horsehead nebula and Belt Stars of Orion

The Horsehead nebula and the Belt Stars of Orion region. This is a 2-frame mosaic using a single Sky90 and a single M25C OSC CCD. H-alpha and OIII data was also included. Imaging time around 4-hours (or more) per frame. This version is with the star reduction app that works with Russ Croman’s StarXTerminator.