[math-fun] Reminder: FactorInteger@1 is {{1, 0}}, or better yet: {}!
Either that, or 1 is a prime number: In[375]:= Cases[FactorInteger@Range@22, {{p_, 1}} -> p] Out[375]= {1, 2, 3, 5, 7, 11, 13, 17, 19} In[376]:= FindSequenceFunction@% Out[376]= FindSequenceFunction[{1, 2, 3, 5, 7, 11, 13, 17, 19}] In[377]:= FindSequenceFunction@Rest@%% Out[377]= Prime You should be embarrassed for all the damage to young students. Who might well ask: Why isn't it {{1,69}}? Can Maple be this stupid? Does it matter? €2,700.00 + €540.00 regular yearly upgrade ?? Macsyma: (c1) MAKELIST(FACTOR_NUMBER(N),N,1,9); 1 1 2 1 1 1 1 3 2 (d1) [[], [2 ], [3 ], [2 ], [5 ], [2 , 3 ], [7 ], [2 ], [3 ]] (c2) BLOCK([FANCY_DISPLAY : FALSE],PLAYBACK([1,2])); --Bill
<< Can Maple be this stupid? >> Mathematica? WFL On 12/29/17, Bill Gosper <billgosper@gmail.com> wrote:
Either that, or 1 is a prime number: In[375]:= Cases[FactorInteger@Range@22, {{p_, 1}} -> p]
Out[375]= {1, 2, 3, 5, 7, 11, 13, 17, 19}
In[376]:= FindSequenceFunction@%
Out[376]= FindSequenceFunction[{1, 2, 3, 5, 7, 11, 13, 17, 19}]
In[377]:= FindSequenceFunction@Rest@%%
Out[377]= Prime
You should be embarrassed for all the damage to young students. Who might well ask: Why isn't it {{1,69}}?
Can Maple be this stupid? Does it matter? €2,700.00 + €540.00 regular yearly upgrade ??
Macsyma: (c1) MAKELIST(FACTOR_NUMBER(N),N,1,9);
1 1 2 1 1 1 1 3 2 (d1) [[], [2 ], [3 ], [2 ], [5 ], [2 , 3 ], [7 ], [2 ], [3 ]]
(c2) BLOCK([FANCY_DISPLAY : FALSE],PLAYBACK([1,2])); --Bill _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Bill Gosper <billgosper@gmail.com> wrote:
Either that, or 1 is a prime number: In[375]:= Cases[FactorInteger@Range@22, {{p_, 1}} -> p]
Out[375]= {1, 2, 3, 5, 7, 11, 13, 17, 19}
In[376]:= FindSequenceFunction@%
Out[376]= FindSequenceFunction[{1, 2, 3, 5, 7, 11, 13, 17, 19}]
In[377]:= FindSequenceFunction@Rest@%%
Out[377]= Prime
You should be embarrassed for all the damage to young students. Who might well ask: Why isn't it {{1,69}}?
Can Maple be this stupid? Does it matter? ???2,700.00 + ???540.00 regular yearly upgrade ??
Macsyma: (c1) MAKELIST(FACTOR_NUMBER(N),N,1,9);
1 1 2 1 1 1 1 3 2 (d1) [[], [2 ], [3 ], [2 ], [5 ], [2 , 3 ], [7 ], [2 ], [3 ]]
(c2) BLOCK([FANCY_DISPLAY : FALSE],PLAYBACK([1,2])); --Bill
-- You received this message because you are subscribed to the Google Groups "mathfuneavesdroppers" group. To unsubscribe from this group and stop receiving emails from it, send an email to mathfuneavesdroppers+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout. There is no problem here. Either definition of "prime" is OK. "1" is not included in the primes if you plan to be using the theorem that an integer is uniquely expressable as a product of primes. In this case you would hardly want to write 6 = 1 x 1 x 1 x ...x 1 x 1 x 2 x 3. Here there could be 46548888235, for example, number of 1's at the front.
If you don't care about this, it would be OK to have 1 be a prime. So it's better to exclude 1 as a prime so this matter can be ignored.
if you plan to be using the theorem that an integer is uniquely expressable as a product of primes
I plan to use this theorem. On Tue, Jan 2, 2018 at 10:37 AM, John Brillhart <jdb@math.arizona.edu> wrote:
Bill Gosper <billgosper@gmail.com> wrote:
Either that, or 1 is a prime number: In[375]:= Cases[FactorInteger@Range@22, {{p_, 1}} -> p]
Out[375]= {1, 2, 3, 5, 7, 11, 13, 17, 19}
In[376]:= FindSequenceFunction@%
Out[376]= FindSequenceFunction[{1, 2, 3, 5, 7, 11, 13, 17, 19}]
In[377]:= FindSequenceFunction@Rest@%%
Out[377]= Prime
You should be embarrassed for all the damage to young students. Who might well ask: Why isn't it {{1,69}}?
Can Maple be this stupid? Does it matter? ???2,700.00 + ???540.00 regular yearly upgrade ??
Macsyma: (c1) MAKELIST(FACTOR_NUMBER(N),N,1,9);
1 1 2 1 1 1 1 3 2 (d1) [[], [2 ], [3 ], [2 ], [5 ], [2 , 3 ], [7 ], [2 ], [3 ]]
(c2) BLOCK([FANCY_DISPLAY : FALSE],PLAYBACK([1,2])); --Bill
-- You received this message because you are subscribed to the Google Groups "mathfuneavesdroppers" group. To unsubscribe from this group and stop receiving emails from it, send an email to mathfuneavesdroppers+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout. There is no problem here. Either definition of "prime" is OK. "1" is not included in the primes if you plan to be using the theorem that an integer is uniquely expressable as a product of primes. In this case you would hardly want to write 6 = 1 x 1 x 1 x ...x 1 x 1 x 2 x 3. Here there could be 46548888235, for example, number of 1's at the front.
If you don't care about this, it would be OK to have 1 be a prime. So it's better to exclude 1 as a prime so this matter can be ignored.
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In the more general context of integral domains, primes are maximal ideals, while the ideal (1) is the entire ring. So indeed, 1 is not a prime. -- Gene On Tuesday, January 2, 2018, 10:43:38 AM PST, Tomas Rokicki <rokicki@gmail.com> wrote:
if you plan to be using the theorem that an integer is uniquely expressable as a product of primes
I plan to use this theorem. On Tue, Jan 2, 2018 at 10:37 AM, John Brillhart <jdb@math.arizona.edu> wrote:
Bill Gosper <billgosper@gmail.com> wrote:
Either that, or 1 is a prime number: In[375]:= Cases[FactorInteger@Range@22, {{p_, 1}} -> p]
Out[375]= {1, 2, 3, 5, 7, 11, 13, 17, 19}
In[376]:= FindSequenceFunction@%
Out[376]= FindSequenceFunction[{1, 2, 3, 5, 7, 11, 13, 17, 19}]
In[377]:= FindSequenceFunction@Rest@%%
Out[377]= Prime
You should be embarrassed for all the damage to young students. Who might well ask: Why isn't it {{1,69}}?
Can Maple be this stupid? Does it matter? ???2,700.00 + ???540.00 regular yearly upgrade ??
Macsyma: (c1) MAKELIST(FACTOR_NUMBER(N),N,1,9);
1 1 2 1 1 1 1 3 2 (d1) [[], [2 ], [3 ], [2 ], [5 ], [2 , 3 ], [7 ], [2 ], [3 ]]
(c2) BLOCK([FANCY_DISPLAY : FALSE],PLAYBACK([1,2])); --Bill
-- You received this message because you are subscribed to the Google Groups "mathfuneavesdroppers" group. To unsubscribe from this group and stop receiving emails from it, send an email to mathfuneavesdroppers+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout. There is no problem here. Either definition of "prime" is OK. "1" is not included in the primes if you plan to be using the theorem that an integer is uniquely expressable as a product of primes. In this case you would hardly want to write 6 = 1 x 1 x 1 x ...x 1 x 1 x 2 x 3. Here there could be 46548888235, for example, number of 1's at the front.
If you don't care about this, it would be OK to have 1 be a prime. So it's better to exclude 1 as a prime so this matter can be ignored.
participants (5)
-
Bill Gosper -
Eugene Salamin -
Fred Lunnon -
John Brillhart -
Tomas Rokicki