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To explain the link given by GH from MO (simply because it may die): Essentially, the computations required to make the proof are known, but their complexity grows exponentially* with increasing $d$. The complexity thereby outruns the capacity of our computers to date at a relatively small value of $d$.

*Accirding to comments (Terry Tao), known algorithms have doubly exponential runtimes, that is $a^{b^d}$ where both $a,b>1$ and the red/blue number is $d$.

To explain the link given by GH from MO (simply because it may die): Essentially, the computations required to make the proof are known, but their complexity grows exponentially* with increasing $d$. The complexity thereby outruns the capacity of our computers to date at a relatively small value of $d$.

*According to comments (Terry Tao), known algorithms have doubly exponential runtimes, that is $a^{b^d}$ where both $a,b>1$ and the red/blue number is $d$.

To explain the link given by GH from MO (simply because it may die): Essentially, the computations required to make the proof are known, but their complexity grows exponentially* with increasing $d$. The complexity thereby outruns the capacity of our computers to date at a relatively small value of $d$.

*According to comments (Terry Tao), known algorithms have doubly exponential runtimes, that is $a^{b^d}$ where both $a,b>1$ and the cap size is $d$.

To explain the link given by GH from MO (simply because it may die): Essentially, the computations required to make the proof are known, but their complexity grows exponentially* with increasing $d$. The complexity thereby outruns the capacity of our computers to date at a relatively small value of $d$.

*Accirding to comments (Terry Tao), known algorithms have doubly exponential runtimes, that is $a^{b^d}$ where both $a,b>1$ and the red/blue number is $d$.

To explain the link given by GH from MO (simply because it may die): Essentially, the computations required to make the proof are known, but their complexity grows exponentially with increasing $d$. The complexity thereby outruns the capacity of our computers to date at a relatively small value of $d$.

To explain the link given by GH from MO (simply because it may die): Essentially, the computations required to make the proof are known, but their complexity grows exponentially* with increasing $d$. The complexity thereby outruns the capacity of our computers to date at a relatively small value of $d$.

*According to comments (Terry Tao), known algorithms have doubly exponential runtimes, that is $a^{b^d}$ where both $a,b>1$ and the cap size is $d$.