How far was base $47$ checked for a generalized Wieferich-prime?
$begingroup$
This question is closely related to :
Wieferich primes in base $47$
but I would like to know the current search limit for this base.
Upto which prime $p$ was $$47^{p-1}equiv 1mod p^2$$ verified ?
Wikipedia only says that no solution is known, but for this particular base I could not find a search limit.
elementary-number-theory reference-request prime-numbers
asked Aug 13 '18 at 9:48
PeterPeter
49k1239136
$endgroup$
add a comment |
$begingroup$
This question is closely related to :
Wieferich primes in base $47$
but I would like to know the current search limit for this base.
Upto which prime $p$ was $$47^{p-1}equiv 1mod p^2$$ verified ?
Wikipedia only says that no solution is known, but for this particular base I could not find a search limit.
elementary-number-theory reference-request prime-numbers
asked Aug 13 '18 at 9:48
PeterPeter
49k1239136
$endgroup$
2
$begingroup$
Here has a list for Wieferich primes of base up to $10125$ and it looks like they have searched up to $1.202E+12$. Also, here lists all the primes of base up to $1052$ and according to Google Translate, for base that has all prime factors smaller than 61, search limit is $9.3E+13$; for base whose largest prime factor is between $67$ and $149$, search limit is $5.58E+13$; for the remaining bases, search limit is $1.202E+13$
$endgroup$
– cortek
Aug 14 '18 at 12:18
add a comment |
$begingroup$
This question is closely related to :
Wieferich primes in base $47$
but I would like to know the current search limit for this base.
Upto which prime $p$ was $$47^{p-1}equiv 1mod p^2$$ verified ?
Wikipedia only says that no solution is known, but for this particular base I could not find a search limit.
elementary-number-theory reference-request prime-numbers
asked Aug 13 '18 at 9:48
PeterPeter
49k1239136
$endgroup$
This question is closely related to :
Wieferich primes in base $47$
but I would like to know the current search limit for this base.
Upto which prime $p$ was $$47^{p-1}equiv 1mod p^2$$ verified ?
Wikipedia only says that no solution is known, but for this particular base I could not find a search limit.
elementary-number-theory reference-request prime-numbers
elementary-number-theory reference-request prime-numbers
asked Aug 13 '18 at 9:48
PeterPeter
49k1239136
asked Aug 13 '18 at 9:48
PeterPeter
49k1239136
asked Aug 13 '18 at 9:48
PeterPeter
49k1239136
asked Aug 13 '18 at 9:48
PeterPeter
49k1239136
asked Aug 13 '18 at 9:48
PeterPeter
49k1239136
49k1239136
2
$begingroup$
Here has a list for Wieferich primes of base up to $10125$ and it looks like they have searched up to $1.202E+12$. Also, here lists all the primes of base up to $1052$ and according to Google Translate, for base that has all prime factors smaller than 61, search limit is $9.3E+13$; for base whose largest prime factor is between $67$ and $149$, search limit is $5.58E+13$; for the remaining bases, search limit is $1.202E+13$
$endgroup$
– cortek
Aug 14 '18 at 12:18
add a comment |
2
$begingroup$
Here has a list for Wieferich primes of base up to $10125$ and it looks like they have searched up to $1.202E+12$. Also, here lists all the primes of base up to $1052$ and according to Google Translate, for base that has all prime factors smaller than 61, search limit is $9.3E+13$; for base whose largest prime factor is between $67$ and $149$, search limit is $5.58E+13$; for the remaining bases, search limit is $1.202E+13$
$endgroup$
– cortek
Aug 14 '18 at 12:18
2
2
$begingroup$
Here has a list for Wieferich primes of base up to $10125$ and it looks like they have searched up to $1.202E+12$. Also, here lists all the primes of base up to $1052$ and according to Google Translate, for base that has all prime factors smaller than 61, search limit is $9.3E+13$; for base whose largest prime factor is between $67$ and $149$, search limit is $5.58E+13$; for the remaining bases, search limit is $1.202E+13$
$endgroup$
– cortek
Aug 14 '18 at 12:18
$begingroup$
Here has a list for Wieferich primes of base up to $10125$ and it looks like they have searched up to $1.202E+12$. Also, here lists all the primes of base up to $1052$ and according to Google Translate, for base that has all prime factors smaller than 61, search limit is $9.3E+13$; for base whose largest prime factor is between $67$ and $149$, search limit is $5.58E+13$; for the remaining bases, search limit is $1.202E+13$
$endgroup$
– cortek
Aug 14 '18 at 12:18
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The link posted in the comments suggests the following (translated from German):
- The bases that have a maximum prime divisor up to $61$ are verified until $9.8 times 10^{13}$,
- The bases that have a maximum prime divisor from $67$ up to $149$ are verified until $6.01 times 10^{13}$,
- The rest is verified until $1.202times10^{13}$.
So it seems that the answer to your question is
Up to $9.8 times 10^{13}$.
answered Jan 14 at 11:59
KlangenKlangen
1,66811334
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
The link posted in the comments suggests the following (translated from German):
- The bases that have a maximum prime divisor up to $61$ are verified until $9.8 times 10^{13}$,
- The bases that have a maximum prime divisor from $67$ up to $149$ are verified until $6.01 times 10^{13}$,
- The rest is verified until $1.202times10^{13}$.
So it seems that the answer to your question is
Up to $9.8 times 10^{13}$.
answered Jan 14 at 11:59
KlangenKlangen
1,66811334
$endgroup$
add a comment |
$begingroup$
The link posted in the comments suggests the following (translated from German):
- The bases that have a maximum prime divisor up to $61$ are verified until $9.8 times 10^{13}$,
- The bases that have a maximum prime divisor from $67$ up to $149$ are verified until $6.01 times 10^{13}$,
- The rest is verified until $1.202times10^{13}$.
So it seems that the answer to your question is
Up to $9.8 times 10^{13}$.
answered Jan 14 at 11:59
KlangenKlangen
1,66811334
$endgroup$
add a comment |
$begingroup$
The link posted in the comments suggests the following (translated from German):
- The bases that have a maximum prime divisor up to $61$ are verified until $9.8 times 10^{13}$,
- The bases that have a maximum prime divisor from $67$ up to $149$ are verified until $6.01 times 10^{13}$,
- The rest is verified until $1.202times10^{13}$.
So it seems that the answer to your question is
Up to $9.8 times 10^{13}$.
answered Jan 14 at 11:59
KlangenKlangen
1,66811334
$endgroup$
The link posted in the comments suggests the following (translated from German):
- The bases that have a maximum prime divisor up to $61$ are verified until $9.8 times 10^{13}$,
- The bases that have a maximum prime divisor from $67$ up to $149$ are verified until $6.01 times 10^{13}$,
- The rest is verified until $1.202times10^{13}$.
So it seems that the answer to your question is
Up to $9.8 times 10^{13}$.
answered Jan 14 at 11:59
KlangenKlangen
1,66811334
answered Jan 14 at 11:59
KlangenKlangen
1,66811334
answered Jan 14 at 11:59
KlangenKlangen
1,66811334
answered Jan 14 at 11:59
KlangenKlangen
1,66811334
1,66811334
add a comment |
add a comment |
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$begingroup$
Here has a list for Wieferich primes of base up to $10125$ and it looks like they have searched up to $1.202E+12$. Also, here lists all the primes of base up to $1052$ and according to Google Translate, for base that has all prime factors smaller than 61, search limit is $9.3E+13$; for base whose largest prime factor is between $67$ and $149$, search limit is $5.58E+13$; for the remaining bases, search limit is $1.202E+13$
$endgroup$
– cortek
Aug 14 '18 at 12:18