And if you're still not convinced the definitive evidence is to run a reasoning model on your own machine.
OpenAI's gpt-oss-20b is a 12GB download for LM Studio from https://lmstudio.ai/models/openai/gpt-oss-20b
It turns out it's powerful enough to solve this. Here's the thinking trace:
We need product. Compute. Use approximate? Let's compute exactly. 87,654,321 * 98,765,432.
We can use multiplication: Let's do 87,654,321 * 98,765,432.
Compute using decomposition: 98,765,432 = 100,000,000 -1,234,568.
So product = 87,654,321100,000,000 - 87,654,3211,234,568.
First term: 8,765,432,100,000,000? Wait multiply: 87,654,321 *100,000,000 = 8,765,432,100,000,000.
Now compute second term: 87,654,321 *1,234,568.
Compute 1,234,568*87,654,321. Use maybe multiply 87,654,321 1,234,568 = 87,654,321(1,200,000+34,568).
First: 1,200,000 = 87,654,32112100,000. 87,654,32112=1,051,851,852? Wait compute: 87,654,321*10=876,543,210; *2=175,308,642; sum =1,051,851,852. Then times100,000 =>105,185,185,200,000.
Second: 34,568. Compute 87,654,32134,568 = 87,654,321*(30,000+4,568).
30,000: 87,654,3213=262,962,963; times10,000 =>2,629,629,630,000.
4,568: compute 87,654,3214,568 = *4000 + *500 + *60 + *8.
4000: 87,654,3214=350,617,284; times1000 =>350,617,284,000.
*500: *5=438,271,605; times100 =>43,827,160,500.
*60: *6=525,925,926; times10 =>5,259,259,260.
*8: 700,834,568? Wait *8=700,834,568.
Sum these: 350,617,284,000
+43,827,160,500 =394,444,444,500
+5,259,259,260 =399,703,703,760
+700,834,568 =400,404,538,328.
Now add *30,000 part: 2,629,629,630,000 +400,404,538,328 =3,030,034,168,328.
Now add to first part: 105,185,185,200,000 +3,030,034,168,328 =108,215,219,368,328.
Thus product second term =108,215,219,368,328.
Now subtract from first term: 8,765,432,100,000,000 -108,215,219,368,328 = 8,657,216,880,631,672.
So answer: 8,657,216,880,631,672.
And a screenshot:
https://gist.github.com/simonw/a8929c0df5f204981652871555420...