We compute the gravity waves induced by anisotropic stresses of stochastic primordial magnetic fields .
The nucleosynthesis bound on gravity waves is then used to derive a limit on the magnetic field amplitude as function of the spectral index .
The obtained limits are extraordinarily strong : If the primordial magnetic field is produced by a causal process , leading to a spectral index n \geq 2 on super horizon scales , galactic magnetic fields produced at the electroweak phase transition or earlier have to be weaker than B _ { \lambda } \leq 10 ^ { -27 } Gauss !
If they are induced during an inflationary phase ( reheating temperature T \sim 10 ^ { 15 } GeV ) with a spectral index n \sim 0 , the magnetic field has to be weaker than B _ { \lambda } \leq 10 ^ { -39 } Gauss !
Only very red magnetic field spectra , n \sim - 3 are not strongly constrained .
We also find that a considerable amount of the magnetic field energy is converted into gravity waves .

The gravity wave limit derived in this work rules out most of the proposed processes for primordial seeds for the large scale magnetic fields observed in galaxies and clusters .