Prime Number Spiral

The number associated with my diurnal age today is a prime number: 27967 and it has the property that it is on the north spoke of a prime number spiral that begins as shown in Figure 1.

Figure 1: source

I thought it might be an interesting challenge for Gemini to write the Python code to generate this spiral up to the largest prime below 40000. To cut a long story short, Gemini failed miserably despite several attempts to improve the code. Grok on the other hand succeeded on its first try although it did time out several times and needed to be reconnected. However, it got the job done and the result is shown in Figure 2 (link to Grok).

Figure 2: code

The formatting is excellent as can be seen in the detail shown in Figure 3 that was taken from Figure 2:

Figure 3: detail from Figure 2

So Gemini proved to be not up to the task despite my persevering with additional prompts whereas Grok succeeded on its first attempt. A lesson learned.