Re: Error: Prime::intpp: Positive integer argument expected in Prime[16.`]

• To: mathgroup at smc.vnet.net
• Subject: [mg61857] Re: Error: Prime::intpp: Positive integer argument expected in Prime[16.`]
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Wed, 2 Nov 2005 04:09:24 -0500 (EST)
• Organization: Uni Leipzig
• References: <dk6vtg\$gi1\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

how do you expect, generate Mathematica Prime[n]??
Do you think it has a general formula, that
generate the n-th prime number and can take the limit n->Infinity
with this formula ?

Mathematica will probably generate finite truncated
approximations of the Sum[] and try to exprapolate the
result. During this procedure it try to compute
Prime[Infinity] or atleast Prime[Overflow[]]
and, bad news, Infinity| Overflow[] is not a
positve integer.

Regards
Jens

"Roger Bagula" <rlbagulatftn at yahoo.com> schrieb im
Newsbeitrag news:dk6vtg\$gi1\$1 at smc.vnet.net...
|I found this sequence of what appears to be
irrational numbers,
| but keep getting this error that doesn't spot a
decent output.
| f[m_] := 1 + Sum[1/m^Prime[n], {n, 1, Infinity}]
| a = Table[N[f[m]], {m, 2, 25}]
| Output={1.41468, 1.15273, 1.07916, 1.04833,
1.03254, 1.02338, 1.01761,
| 1.01373,  1.01101, 1.00902, 1.00753, 1.00638,
1.00547, 1.00474, 1.00415,
| 1.00366, 1.00326, 1.00292, 1.00263, 1.00238,
1.00216, 1.00197, 1.00181,
| 1.00166}
| \!\(\*
|   RowBox[{
|     RowBox[{\(rime::"intpp"\), ":", " ",
|     "\<\"Positive integer argument expected in
Prime[
|       16.`]. \\!\\( \\*ButtonBox[\\(Moreâ?¦\\),
\
| ButtonData:>\\\"Prime::intpp\\\",
| ButtonFrame->\\\"None\\\"]\\)\"\>"}], "\n",
|     RowBox[{\(Prime::"intpp"\), ":", " ",
"\<\"Positive integer argument \
| expected in Prime[16.`]. \\!\\(
\\*ButtonBox[\\(Moreâ?¦\\), \
| ButtonData:>\\\"Prime::intpp\\\",
| ButtonFrame->\\\"None\\\"]\\)\"\>"}], "\n",
|     RowBox[{\(Prime::"intpp"\), ":", " ",
|      "\<\"Positive integer argument expected in
Prime[
|       17.`]. \\!\\( \\*ButtonBox[\\(Moreâ?¦\\),
\
| ButtonData:>\\\"Prime::intpp\\\",
| ButtonFrame->\\\"None\\\"]\\)\"\>"}], "\n",
|     RowBox[{\(General::"stop"\), \(\(:\)\(\
\)\), "\<\"Further output of \
| Prime::\"\>", "intpp", "\<\" will be suppressed
during this calculation. \
| \\!\\( \\*ButtonBox[\\(Moreâ?¦\\),
ButtonData:>\\\"General::stop\\\", \
|      ButtonFrame->\\\"None\\\"]\\)\"\>"}]}]\)
| More gives:
| â?¼ Generated when the indicated argument used
in Prime is not a positive
| integer.
|

```