To estimate the total number of FLOPs required to train GPT-3, we use the following reasoning:

1. FLOPs Formula: For transformer-based models, a common approximation is:
   [ \text{FLOPs} \approx 6 \times \text{number of parameters} \times \text{number of tokens} ]
   The factor of 6 accounts for 2 FLOPs per parameter in the forward pass (matrix multiplications) and 4 FLOPs per parameter in the backward pass (gradient calculations), totaling 6 FLOPs per parameter per token.

2. GPT-3 Parameters: The largest GPT-3 model has 175 billion parameters ((1.75 \times 10^{11})).

3. Training Tokens: GPT-3 was trained on approximately 300 billion tokens ((3 \times 10^{11})), as indicated in its original paper.

4. Calculation:
   [ \text{FLOPs} \approx 6 \times (1.75 \times 10^{11}) \times (3 \times 10^{11}) = 3.15 \times 10^{23} , \text{FLOPs}. ]

5. Uncertainty: The exact token count and FLOPs factor can vary slightly, but this estimate aligns with widely cited values (e.g., ~(3.14 \times 10^{23}) FLOPs).

Final Estimate:
Training GPT-3 required approximately (3.1 \times 10^{23}) FLOPs.