It is easily seen as not prime since all of its digits sum to a multiple of three.Ann wrote: ↑Sat Mar 27, 2021 5:47 pm I think of it like this. A white dwarf is made of prime fuel. Well, not prime fuel, because only hydrogen is prime fuel, and most white dwarfs are made of helium, carbon and oxygen. (I think.)
So a white dwarf is not made of prime fuel, but "good enough fuel".
Weigh a white dwarf down more than its electron degeneracy can bear, and it will ignite. And then, all that good enough fuel will go ka-poof!!!!
Ann
Hey, I like the number of this post. I missed my 11111th post, but a post number 11211 is not bad, either.
Is it a prime number?
APOD: The Medusa Nebula (2021 Mar 26)
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Re: APOD: The Medusa Nebula (2021 Mar 26)
Chris
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Re: APOD: The Medusa Nebula (2021 Mar 26)
In short: less massive white dwarfs blow off their outer layers in repeated novas as a result of accretion, whereas more massive white dwarfs accumulate enough to collapse under degeneracy pressure and become supernovas, but somehow avoid becoming mere novas. Why can't they also become novas? Why must they wait for more mass and thereby become supernovas?Ann wrote: ↑Sat Mar 27, 2021 5:47 pm I think of it like this. A white dwarf is made of prime fuel. Well, not prime fuel, because only hydrogen is prime fuel, and most white dwarfs are made of helium, carbon and oxygen. (I think.)
So a white dwarf is not made of prime fuel, but "good enough fuel".
Weigh a white dwarf down more than its electron degeneracy can bear, and it will ignite. And then, all that good enough fuel will go ka-poof!!!!
Ann
Hey, I like the number of this post. I missed my 11111th post, but a post number 11211 is not bad, either.
Is it a prime number?
--
"To B̬̻̋̚o̞̮̚̚l̘̲̀᷾d̫͓᷅ͩḷ̯᷁ͮȳ͙᷊͠ Go......Beyond The F͇̤i̙̖e̤̟l̡͓d͈̹s̙͚ We Know."{ʲₒʰₙNYᵈₑᵉₚ}
"To B̬̻̋̚o̞̮̚̚l̘̲̀᷾d̫͓᷅ͩḷ̯᷁ͮȳ͙᷊͠ Go......Beyond The F͇̤i̙̖e̤̟l̡͓d͈̹s̙͚ We Know."{ʲₒʰₙNYᵈₑᵉₚ}
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Re: APOD: The Medusa Nebula (2021 Mar 26)
Wish I knew, Johnny. So let me speculate.johnnydeep wrote: ↑Sat Mar 27, 2021 6:21 pmIn short: less massive white dwarfs blow off their outer layers in repeated novas as a result of accretion, whereas more massive white dwarfs accumulate enough to collapse under degeneracy pressure and become supernovas, but somehow avoid becoming mere novas. Why can't they also become novas? Why must they wait for more mass and thereby become supernovas?Ann wrote: ↑Sat Mar 27, 2021 5:47 pm I think of it like this. A white dwarf is made of prime fuel. Well, not prime fuel, because only hydrogen is prime fuel, and most white dwarfs are made of helium, carbon and oxygen. (I think.)
So a white dwarf is not made of prime fuel, but "good enough fuel".
Weigh a white dwarf down more than its electron degeneracy can bear, and it will ignite. And then, all that good enough fuel will go ka-poof!!!!
Ann
Hey, I like the number of this post. I missed my 11111th post, but a post number 11211 is not bad, either.
Is it a prime number?
The surface gravity of a white dwarf is very high indeed. So when a gob of gas from a red giant crashes down onto the surface of a white dwarf, it's going to make a big crash indeed. Move over, asteroid that killed the dinosaurs.
Perhaps, if the crash that happens when a gob of gas slams onto the surface of the white dwarf is sufficiently big, maybe the gas that falls onto the surface of the white dwarf will just explode? Like a nova, you know?
Click to play embedded YouTube video.
Ann
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Re: APOD: The Medusa Nebula (2021 Mar 26)
Yeah, perhaps it’s still all (and only) about the mass. And perhaps also the accretion rate, since I don’t think of gas accreting in discrete gobs, but in a continual process. I still need to read up on all this stuff, but not today since I’m running on literally zero sleep after an emergency molar tooth extraction late yesterday. Kept fearing I would bleed to death in my sleep, which kept me from falling to it (sleep , that is). TMI?Ann wrote: ↑Sat Mar 27, 2021 6:44 pmWish I knew, Johnny. So let me speculate.johnnydeep wrote: ↑Sat Mar 27, 2021 6:21 pmIn short: less massive white dwarfs blow off their outer layers in repeated novas as a result of accretion, whereas more massive white dwarfs accumulate enough to collapse under degeneracy pressure and become supernovas, but somehow avoid becoming mere novas. Why can't they also become novas? Why must they wait for more mass and thereby become supernovas?Ann wrote: ↑Sat Mar 27, 2021 5:47 pm I think of it like this. A white dwarf is made of prime fuel. Well, not prime fuel, because only hydrogen is prime fuel, and most white dwarfs are made of helium, carbon and oxygen. (I think.)
So a white dwarf is not made of prime fuel, but "good enough fuel".
Weigh a white dwarf down more than its electron degeneracy can bear, and it will ignite. And then, all that good enough fuel will go ka-poof!!!!
Ann
Hey, I like the number of this post. I missed my 11111th post, but a post number 11211 is not bad, either.
Is it a prime number?
The surface gravity of a white dwarf is very high indeed. So when a gob of gas from a red giant crashes down onto the surface of a white dwarf, it's going to make a big crash indeed. Move over, asteroid that killed the dinosaurs.
Perhaps, if the crash that happens when a gob of gas slams onto the surface of the white dwarf is sufficiently big, maybe the gas that falls onto the surface of the white dwarf will just explode? Like a nova, you know?
But if a white dwarf is massive enough to be close to its Chandrasekhar limit, then maybe the entire white dwarf gets sufficiently unsettled to blow itself to smithereens, if just one more gob of gas falls onto it? Like when the obese and sickeningly full Mr. Creosote of Monty Python's The Meaning of Life is persuaded to eat just one after dinner mint and starts vomiting rivers of puke on all and sundry around him.Click to play embedded YouTube video.
Ann
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"To B̬̻̋̚o̞̮̚̚l̘̲̀᷾d̫͓᷅ͩḷ̯᷁ͮȳ͙᷊͠ Go......Beyond The F͇̤i̙̖e̤̟l̡͓d͈̹s̙͚ We Know."{ʲₒʰₙNYᵈₑᵉₚ}
"To B̬̻̋̚o̞̮̚̚l̘̲̀᷾d̫͓᷅ͩḷ̯᷁ͮȳ͙᷊͠ Go......Beyond The F͇̤i̙̖e̤̟l̡͓d͈̹s̙͚ We Know."{ʲₒʰₙNYᵈₑᵉₚ}
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Re: APOD: The Medusa Nebula (2021 Mar 26)
Sounds pretty awful. Hope you'll have a good night's sleep and feel better tomorrow.johnnydeep wrote: ↑Sat Mar 27, 2021 7:11 pm
Yeah, perhaps it’s still all (and only) about the mass. And perhaps also the accretion rate, since I don’t think of gas accreting in discrete gobs, but in a continual process. I still need to read up on all this stuff, but not today since I’m running on literally zero sleep after an emergency molar tooth extraction late yesterday. Kept fearing I would bleed to death in my sleep, which kept me from falling to it (sleep , that is). TMI?
Ann
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Re: APOD: The Medusa Nebula (2021 Mar 26)
Thanks. Feeling much better today, after 10 hours of restful sleep. Now, on to tackle novas and supernovas!Ann wrote: ↑Sat Mar 27, 2021 7:30 pmSounds pretty awful. Hope you'll have a good night's sleep and feel better tomorrow.johnnydeep wrote: ↑Sat Mar 27, 2021 7:11 pm
Yeah, perhaps it’s still all (and only) about the mass. And perhaps also the accretion rate, since I don’t think of gas accreting in discrete gobs, but in a continual process. I still need to read up on all this stuff, but not today since I’m running on literally zero sleep after an emergency molar tooth extraction late yesterday. Kept fearing I would bleed to death in my sleep, which kept me from falling to it (sleep , that is). TMI?
Ann
--
"To B̬̻̋̚o̞̮̚̚l̘̲̀᷾d̫͓᷅ͩḷ̯᷁ͮȳ͙᷊͠ Go......Beyond The F͇̤i̙̖e̤̟l̡͓d͈̹s̙͚ We Know."{ʲₒʰₙNYᵈₑᵉₚ}
"To B̬̻̋̚o̞̮̚̚l̘̲̀᷾d̫͓᷅ͩḷ̯᷁ͮȳ͙᷊͠ Go......Beyond The F͇̤i̙̖e̤̟l̡͓d͈̹s̙͚ We Know."{ʲₒʰₙNYᵈₑᵉₚ}
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Re: APOD: The Medusa Nebula (2021 Mar 26)
Very good to hear that you are feeling better, Johnny! Then you may be up for this: A "failed supernova" that just may have been something in between a classical nova, where only the newly accreted material on the surface of a white dwarf is blown off, and a type Ia supernova, in which the entire white dwarf annihilates itself.
So SN 2008ha may have been an explosion where a part of the white dwarf was destroyed, but not all of it. Very interesting, if you ask me!
Ann
ESA/Hubble wrote:
In November 2008, 14-year-old Caroline Moore from New York discovered a supernova in UGC 12682. This made her the youngest person at the time to have discovered a supernova. Follow-up observations by professional astronomers of the so-called SN 2008ha showed that it was peculiarly interesting in many different ways: its host galaxy UGC 12682 rarely produces supernovae. It is one of the faintest supernovae ever observed and after the explosion it expanded very slowly, suggesting that the explosion did not release copious amounts of energy as usually expected.
Astronomers have now classified SN 2008ha as a subclass of a Type Ia supernova, which is the explosion of a white dwarf that hungrily accretes matter from a companion star. SN 2008ha may have been the result of a partially failed supernova, explaining why the explosion failed to decimate the whole star.
So SN 2008ha may have been an explosion where a part of the white dwarf was destroyed, but not all of it. Very interesting, if you ask me!
Ann
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Re: APOD: The Medusa Nebula (2021 Mar 26)
Nope, at least according to the prime number calculator...Ann wrote: ↑Sat Mar 27, 2021 5:47 pm I think of it like this. A white dwarf is made of prime fuel. Well, not prime fuel, because only hydrogen is prime fuel, and most white dwarfs are made of helium, carbon and oxygen. (I think.)
So a white dwarf is not made of prime fuel, but "good enough fuel".
Weigh a white dwarf down more than its electron degeneracy can bear, and it will ignite. And then, all that good enough fuel will go ka-poof!!!!
Ann
Hey, I like the number of this post. I missed my 11111th post, but a post number 11211 is not bad, either.
Is it a prime number?
https://www.calculatorsoup.com/calculat ... ulator.php11211 is a Composite Number and can be factored by any of the following numbers.
All the factors of 11211 :
1, 3, 37, 101, 111, 303, 3737, 11211
Warning: it is very addictive!
Eric
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Re: APOD: The Medusa Nebula (2021 Mar 26)
Yes, pretty interesting. It seems no matter how unusual the phenomenon, there is always something even more unusual!Ann wrote: ↑Mon Mar 29, 2021 5:08 am Very good to hear that you are feeling better, Johnny! Then you may be up for this: A "failed supernova" that just may have been something in between a classical nova, where only the newly accreted material on the surface of a white dwarf is blown off, and a type Ia supernova, in which the entire white dwarf annihilates itself.
ESA/Hubble wrote:
In November 2008, 14-year-old Caroline Moore from New York discovered a supernova in UGC 12682. This made her the youngest person at the time to have discovered a supernova. Follow-up observations by professional astronomers of the so-called SN 2008ha showed that it was peculiarly interesting in many different ways: its host galaxy UGC 12682 rarely produces supernovae. It is one of the faintest supernovae ever observed and after the explosion it expanded very slowly, suggesting that the explosion did not release copious amounts of energy as usually expected.
Astronomers have now classified SN 2008ha as a subclass of a Type Ia supernova, which is the explosion of a white dwarf that hungrily accretes matter from a companion star. SN 2008ha may have been the result of a partially failed supernova, explaining why the explosion failed to decimate the whole star.
So SN 2008ha may have been an explosion where a part of the white dwarf was destroyed, but not all of it. Very interesting, if you ask me!
Ann
--
"To B̬̻̋̚o̞̮̚̚l̘̲̀᷾d̫͓᷅ͩḷ̯᷁ͮȳ͙᷊͠ Go......Beyond The F͇̤i̙̖e̤̟l̡͓d͈̹s̙͚ We Know."{ʲₒʰₙNYᵈₑᵉₚ}
"To B̬̻̋̚o̞̮̚̚l̘̲̀᷾d̫͓᷅ͩḷ̯᷁ͮȳ͙᷊͠ Go......Beyond The F͇̤i̙̖e̤̟l̡͓d͈̹s̙͚ We Know."{ʲₒʰₙNYᵈₑᵉₚ}
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Re: APOD: The Medusa Nebula (2021 Mar 26)
XgeoX wrote: ↑Mon Mar 29, 2021 2:38 pmhttps://www.calculatorsoup.com/calculat ... ulator.php11211 is a Composite Number and can be factored by any of the following numbers.
All the factors of 11211 :
1, 3, 37, 101, 111, 303, 3737, 11211
Warning: it is very addictive!
https://en.wikipedia.org/wiki/Sexy_prime wrote:
<<Sexy primes are prime numbers that differ from each other by 6.
As of October 2019, the largest-known pair of sexy primes was found by P. Kaiser and has 50,539 digits. The primes are:
- Sexy primes below 500 are:
(5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97,103), (101,107), (103,109), (107,113), (131,137), (151,157), (157,163), (167,173), (173,179), (191,197), (193,199), (223,229), (227,233), (233,239), (251,257), (257,263), (263,269), (271,277), (277,283), (307,313), (311,317), (331,337), (347,353), (353,359), (367,373), (373,379), (383,389), (433,439), (443,449), (457,463), (461,467).
...............................................................
- p = (520461 × 255931+1) × (98569639289 × (520461 × 255931-1)2-3)-1
p+6 = (520461 × 255931+1) × (98569639289 × (520461 × 255931-1)2-3)+5
Sexy primes can be extended to larger constellations.
E.g., triplets of primes (p, p+6, p+12) such that p+18 is composite are called sexy prime triplets.
in December Norman Luhn & Gerd Lamprecht & Norman Luhn set a record for the largest-known sexy prime triplet with 10,602 digits:
- Sexy prime triplets below 1,000 are:
(7,13,19), (17,23,29), (31,37,43), (47,53,59), (67,73,79), (97,103,109), (101,107,113), (151,157,163), (167,173,179), (227,233,239), (257,263,269), (271,277,283), (347,353,359), (367,373,379), (557,563,569), (587,593,599), (607,613,619), (647,653,659), (727,733,739), (941,947,953), (971,977,983).
>>
- p = 2683143625525 x 235176+1.
p+6 = 2683143625525 x 235176+7.
p+12 = 2683143625525 x 235176+13.
Art Neuendorffer
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Re: APOD: The Medusa Nebula (2021 Mar 26)
Sometimes mathematicians appear to have too much time on their hands. Sexy Primes seem particularly useless to me, let alone "sexy", and not really even very interesting. Same for "sexy prime triples". Perhaps that's why I abandoned the idea of becoming a professional mathematician after getting an MS in math. Now, consecutive primes {p,p+6} (that is, with no intervening primes), or consecuting primes {p,p+n} for various values of n do seem interesting. And even more interesting is the "primorial" function, which extends the idea of the factorial to the multiplication of all primes up to and including n. See https://en.wikipedia.org/wiki/Primorialneufer wrote: ↑Tue Mar 30, 2021 2:09 amXgeoX wrote: ↑Mon Mar 29, 2021 2:38 pmhttps://www.calculatorsoup.com/calculat ... ulator.php11211 is a Composite Number and can be factored by any of the following numbers.
All the factors of 11211 :
1, 3, 37, 101, 111, 303, 3737, 11211
Warning: it is very addictive!https://en.wikipedia.org/wiki/Sexy_prime wrote:
<<Sexy primes are prime numbers that differ from each other by 6.
As of October 2019, the largest-known pair of sexy primes was found by P. Kaiser and has 50,539 digits. The primes are:
- Sexy primes below 500 are:
(5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97,103), (101,107), (103,109), (107,113), (131,137), (151,157), (157,163), (167,173), (173,179), (191,197), (193,199), (223,229), (227,233), (233,239), (251,257), (257,263), (263,269), (271,277), (277,283), (307,313), (311,317), (331,337), (347,353), (353,359), (367,373), (373,379), (383,389), (433,439), (443,449), (457,463), (461,467).
...............................................................
- p = (520461 × 255931+1) × (98569639289 × (520461 × 255931-1)2-3)-1
p+6 = (520461 × 255931+1) × (98569639289 × (520461 × 255931-1)2-3)+5
Sexy primes can be extended to larger constellations.
E.g., triplets of primes (p, p+6, p+12) such that p+18 is composite are called sexy prime triplets.
in December Norman Luhn & Gerd Lamprecht & Norman Luhn set a record for the largest-known sexy prime triplet with 10,602 digits:
- Sexy prime triplets below 1,000 are:
(7,13,19), (17,23,29), (31,37,43), (47,53,59), (67,73,79), (97,103,109), (101,107,113), (151,157,163), (167,173,179), (227,233,239), (257,263,269), (271,277,283), (347,353,359), (367,373,379), (557,563,569), (587,593,599), (607,613,619), (647,653,659), (727,733,739), (941,947,953), (971,977,983).
>>
- p = 2683143625525 x 235176+1.
p+6 = 2683143625525 x 235176+7.
p+12 = 2683143625525 x 235176+13.
--
"To B̬̻̋̚o̞̮̚̚l̘̲̀᷾d̫͓᷅ͩḷ̯᷁ͮȳ͙᷊͠ Go......Beyond The F͇̤i̙̖e̤̟l̡͓d͈̹s̙͚ We Know."{ʲₒʰₙNYᵈₑᵉₚ}
"To B̬̻̋̚o̞̮̚̚l̘̲̀᷾d̫͓᷅ͩḷ̯᷁ͮȳ͙᷊͠ Go......Beyond The F͇̤i̙̖e̤̟l̡͓d͈̹s̙͚ We Know."{ʲₒʰₙNYᵈₑᵉₚ}