Re: [math-fun] (Silly) Q to WolframAlpha
My Mma gives: PrimeQ[1699246750872437141327603] (*??*) False FactorInteger[1699246750872437141327603] {{7, 1}, {242749535838919591618229, 1}} NextPrime[1699246750872437141327603, -1] 1699246750872437141327467 NextPrime[1699246750872437141327467] 1699246750872437141327609 ========= May be it's misprint: 1699246750872437141327609, not 1699246750872437141327603 ?
Воскресенье, 29 мая 2016, 14:00 +03:00 от "Adam P. Goucher" <apgoucher@gmx.com>:
Well, the largest known computation of PrimePi is:
PrimePi[10^26] = 1699246750872437141327603
(see https://dalspace.library.dal.ca/handle/10222/60524 )
By using Nest[NextPrime, 10^26, 10^7], this allows one to compute:
p_1699246750872437151327603 = 100000000000000000598602537
in an epic 40-minute corollary-snipe. I claim this is currently the largest known prime number with known index -- but of course you can break this record instantly by using NextPrime.
Best wishes,
Adam P. Goucher
Sent: Sunday, May 29, 2016 at 9:05 AM From: "Zak Seidov via math-fun" < math-fun@mailman.xmission.com > To: math-fun < math-fun@mailman.xmission.com > Subject: [math-fun] (Silly) Q to WolframAlpha
Q: What is known largest prime number with known index? A1: There is no largest prime. A2: 2^74207281-1 (as of April 2016)
? May I ask you gurus: Q: What is known largest prime number with known index? (e.g., as of 29.05.16 or smth) Zak _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
PARI gives the same (04:19) gp > p = 1699246750872437141327603;isprime(p) time = 63 ms. %1 = 0 (04:19) gp > factor(p) time = 63 ms. %2 =[7 1] [242749535838919591618229 1] (04:19) gp > nextprime(p) %3 = 1699246750872437141327609 (04:20) gp > precprime(p) %4 = 1699246750872437141327467 (04:20) gp > nextprime(%+1) %6 = 1699246750872437141327609 (04:21) gp
Понедельник, 30 мая 2016, 4:09 +03:00 от Zak Seidov via math-fun <math-fun@mailman.xmission.com>:
My Mma gives:
PrimeQ[1699246750872437141327603] (*??*) False
FactorInteger[1699246750872437141327603] {{7, 1}, {242749535838919591618229, 1}}
NextPrime[1699246750872437141327603, -1] 1699246750872437141327467
NextPrime[1699246750872437141327467] 1699246750872437141327609 ========= May be it's misprint: 1699246750872437141327609, not 1699246750872437141327603 ?
Воскресенье, 29 мая 2016, 14:00 +03:00 от "Adam P. Goucher" < apgoucher@gmx.com >:
Well, the largest known computation of PrimePi is:
PrimePi[10^26] = 1699246750872437141327603
(see https://dalspace.library.dal.ca/handle/10222/60524 )
By using Nest[NextPrime, 10^26, 10^7], this allows one to compute:
p_1699246750872437151327603 = 100000000000000000598602537
in an epic 40-minute corollary-snipe. I claim this is currently the largest known prime number with known index -- but of course you can break this record instantly by using NextPrime.
Best wishes,
Adam P. Goucher
Sent: Sunday, May 29, 2016 at 9:05 AM From: "Zak Seidov via math-fun" < math-fun@mailman.xmission.com > To: math-fun < math-fun@mailman.xmission.com > Subject: [math-fun] (Silly) Q to WolframAlpha
Q: What is known largest prime number with known index? A1: There is no largest prime. A2: 2^74207281-1 (as of April 2016)
? May I ask you gurus: Q: What is known largest prime number with known index? (e.g., as of 29.05.16 or smth) Zak _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Zak: You're misreading Adam quoted fact
PrimePi[10^26] = 1699246750872437141327603
This means that there are exactly 1699246750872437141327603 primes less than (or equal to) 10^26. --Michael On Sun, May 29, 2016 at 9:25 PM, Zak Seidov <math-fun@mailman.xmission.com> wrote:
PARI gives the same
(04:19) gp > p = 1699246750872437141327603;isprime(p) time = 63 ms. %1 = 0 (04:19) gp > factor(p) time = 63 ms. %2 =[7 1] [242749535838919591618229 1] (04:19) gp > nextprime(p) %3 = 1699246750872437141327609 (04:20) gp > precprime(p) %4 = 1699246750872437141327467 (04:20) gp > nextprime(%+1) %6 = 1699246750872437141327609 (04:21) gp
Понедельник, 30 мая 2016, 4:09 +03:00 от Zak Seidov via math-fun < math-fun@mailman.xmission.com>:
My Mma gives:
PrimeQ[1699246750872437141327603] (*??*) False
FactorInteger[1699246750872437141327603] {{7, 1}, {242749535838919591618229, 1}}
NextPrime[1699246750872437141327603, -1] 1699246750872437141327467
NextPrime[1699246750872437141327467] 1699246750872437141327609 ========= May be it's misprint: 1699246750872437141327609, not 1699246750872437141327603 ?
Воскресенье, 29 мая 2016, 14:00 +03:00 от "Adam P. Goucher" < apgoucher@gmx.com >:
Well, the largest known computation of PrimePi is:
PrimePi[10^26] = 1699246750872437141327603
(see https://dalspace.library.dal.ca/handle/10222/60524 )
By using Nest[NextPrime, 10^26, 10^7], this allows one to compute:
p_1699246750872437151327603 = 100000000000000000598602537
in an epic 40-minute corollary-snipe. I claim this is currently the largest known prime number with known index -- but of course you can break this record instantly by using NextPrime.
Best wishes,
Adam P. Goucher
Sent: Sunday, May 29, 2016 at 9:05 AM From: "Zak Seidov via math-fun" < math-fun@mailman.xmission.com > To: math-fun < math-fun@mailman.xmission.com > Subject: [math-fun] (Silly) Q to WolframAlpha
Q: What is known largest prime number with known index? A1: There is no largest prime. A2: 2^74207281-1 (as of April 2016)
? May I ask you gurus: Q: What is known largest prime number with known index? (e.g., as of 29.05.16 or smth)
Zak _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
I'm so sorry:( I've just discovered my err seconds before your message:( And what is the prime(10^26 or whatever large), then?
Понедельник, 30 мая 2016, 4:40 +03:00 от Michael Kleber <michael.kleber@gmail.com>:
Zak: You're misreading Adam quoted fact
PrimePi[10^26] = 1699246750872437141327603
This means that there are exactly 1699246750872437141327603 primes less than (or equal to) 10^26.
--Michael
On Sun, May 29, 2016 at 9:25 PM, Zak Seidov < math-fun@mailman.xmission.com > wrote:
PARI gives the same
(04:19) gp > p = 1699246750872437141327603;isprime(p) time = 63 ms. %1 = 0 (04:19) gp > factor(p) time = 63 ms. %2 =[7 1] [242749535838919591618229 1] (04:19) gp > nextprime(p) %3 = 1699246750872437141327609 (04:20) gp > precprime(p) %4 = 1699246750872437141327467 (04:20) gp > nextprime(%+1) %6 = 1699246750872437141327609 (04:21) gp
Понедельник, 30 мая 2016, 4:09 +03:00 от Zak Seidov via math-fun < math-fun@mailman.xmission.com >:
My Mma gives:
PrimeQ[1699246750872437141327603] (*??*) False
FactorInteger[1699246750872437141327603] {{7, 1}, {242749535838919591618229, 1}}
NextPrime[1699246750872437141327603, -1] 1699246750872437141327467
NextPrime[1699246750872437141327467] 1699246750872437141327609 ========= May be it's misprint: 1699246750872437141327609, not 1699246750872437141327603 ?
Воскресенье, 29 мая 2016, 14:00 +03:00 от "Adam P. Goucher" < apgoucher@gmx.com >:
Well, the largest known computation of PrimePi is:
PrimePi[10^26] = 1699246750872437141327603
(see https://dalspace.library.dal.ca/handle/10222/60524 )
By using Nest[NextPrime, 10^26, 10^7], this allows one to compute:
p_1699246750872437151327603 = 100000000000000000598602537
in an epic 40-minute corollary-snipe. I claim this is currently the largest known prime number with known index -- but of course you can break this record instantly by using NextPrime.
Best wishes,
Adam P. Goucher
Sent: Sunday, May 29, 2016 at 9:05 AM From: "Zak Seidov via math-fun" < math-fun@mailman.xmission.com > To: math-fun < math-fun@mailman.xmission.com > Subject: [math-fun] (Silly) Q to WolframAlpha
Q: What is known largest prime number with known index? A1: There is no largest prime. A2: 2^74207281-1 (as of April 2016)
? May I ask you gurus: Q: What is known largest prime number with known index? (e.g., as of 29.05.16 or smth) Zak _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
NextPrime[10^26, -1] 99999999999999999999999859 So : Prime[1699246750872437141327603]=99999999999999999999999859 Prime[1699246750872437141327604]=100000000000000000000000067 or another my "mea culpa" :(
Понедельник, 30 мая 2016, 4:45 +03:00 от Zak Seidov via math-fun <math-fun@mailman.xmission.com>:
I'm so sorry:( I've just discovered my err seconds before your message:( And what is the prime(10^26 or whatever large), then?
Понедельник, 30 мая 2016, 4:40 +03:00 от Michael Kleber < michael.kleber@gmail.com >:
Zak: You're misreading Adam quoted fact
PrimePi[10^26] = 1699246750872437141327603
This means that there are exactly 1699246750872437141327603 primes less than (or equal to) 10^26.
--Michael
On Sun, May 29, 2016 at 9:25 PM, Zak Seidov < math-fun@mailman.xmission.com > wrote:
PARI gives the same
(04:19) gp > p = 1699246750872437141327603;isprime(p) time = 63 ms. %1 = 0 (04:19) gp > factor(p) time = 63 ms. %2 =[7 1] [242749535838919591618229 1] (04:19) gp > nextprime(p) %3 = 1699246750872437141327609 (04:20) gp > precprime(p) %4 = 1699246750872437141327467 (04:20) gp > nextprime(%+1) %6 = 1699246750872437141327609 (04:21) gp
Понедельник, 30 мая 2016, 4:09 +03:00 от Zak Seidov via math-fun < math-fun@mailman.xmission.com >:
My Mma gives:
PrimeQ[1699246750872437141327603] (*??*) False
FactorInteger[1699246750872437141327603] {{7, 1}, {242749535838919591618229, 1}}
NextPrime[1699246750872437141327603, -1] 1699246750872437141327467
NextPrime[1699246750872437141327467] 1699246750872437141327609 ========= May be it's misprint: 1699246750872437141327609, not 1699246750872437141327603 ?
Воскресенье, 29 мая 2016, 14:00 +03:00 от "Adam P. Goucher" < apgoucher@gmx.com >:
Well, the largest known computation of PrimePi is:
PrimePi[10^26] = 1699246750872437141327603
(see https://dalspace.library.dal.ca/handle/10222/60524 )
By using Nest[NextPrime, 10^26, 10^7], this allows one to compute:
p_1699246750872437151327603 = 100000000000000000598602537
in an epic 40-minute corollary-snipe. I claim this is currently the largest known prime number with known index -- but of course you can break this record instantly by using NextPrime.
Best wishes,
Adam P. Goucher
Sent: Sunday, May 29, 2016 at 9:05 AM From: "Zak Seidov via math-fun" < math-fun@mailman.xmission.com > To: math-fun < math-fun@mailman.xmission.com > Subject: [math-fun] (Silly) Q to WolframAlpha
Q: What is known largest prime number with known index? A1: There is no largest prime. A2: 2^74207281-1 (as of April 2016)
? May I ask you gurus: Q: What is known largest prime number with known index? (e.g., as of 29.05.16 or smth) Zak _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Zak Seidov