0 4   7 -11 -17  19
  1 3   7  11 -13
  2 4   5   7  17 -19
  3 4   2  -7 -11  13
  4 1   2
  5 2   3  -2
  6 ?
  7 ?
  8 4   3  -7 -11  13
  9 1   3
 10 4   3   7  11 -13
 11 4  -2  -3  -5   7
 12 3  -2  -3   5
 13 2   3   2
 14 4  -3  -5 -11  13
 15 3  -3  -5   7
 16 2   5  -3
 17 ?
 18 ?
 19 4   2  -3  -5   7
 20 3   2  -3   5
 21 2   5  -2
 22 4  -5 -11 -19  23
 23 3  -5 -11  13
 24 2   7  -5
 25 1   5
 26 4   5   7  11 -13
 27 4   2  -5 -11  13
 28 3   2  -5   7
 29 2   5   2
 30 3  -2   3   5
 31 ?
 32 4   3  -5 -11  13
 33 3   3  -5   7
 34 2   5   3
 35 4  -2  -3 -11  13
 36 3  -2  -3   7
 37 4   2   3  -5   7
 38 3   2   3   5
 39 3  -3 -11  13
 40 2   7  -3
 41 ?
 42 ?
 43 4   2  -3 -11  13
 44 3   2  -3   7
 45 2   7  -2
 46 4  -5  -7 -13  17
 47 3  -5  -7  11
 48 2  13 -11
 49 1   7
 50 4   7  11  13 -17
 51 4   2  -5  -7  11
 52 3   2 -11  13
 53 2   7   2
 54 3  -2   3   7
 55 ?
 56 4   3  -5  -7  11
 57 3   3 -11  13
 58 2   7   3
 59 4  -2  -3  -7  11
 60 ?
 61 4  -2  -3   5   7
 62 3   2   3   7
 63 3  -3  -7  11
 64 4  -3   5 -11  13
 65 3  -3   5   7
 66 ?
 67 4   2  -3  -7  11
 68 3  -2  -7  11
 69 4   2  -3   5   7
 70 3  -2   5   7
 71 3  -7 -13  17
 72 2  11  -7
 73 3   5 -11  13
 74 2   7   5
 75 4   2  -7 -13  17
 76 3   2  -7  11
 77 4  -2   3  -7  11
 78 3   2   5   7
 79 4  -2   3   5   7
 80 4   3  -7 -13  17
 81 3   3  -7  11
 82 4   3   5 -11  13
 83 3   3   5   7
 84 ?
 85 4   2   3  -7  11
 86 4  -3  -5  -7  13
 87 3  -3  -5  11
 88 4  -3   5  -7  11
 89 ?
 90 ?
 91 4   2  -3  -5  11
 92 3  -2  -5  11
 93 4  -2   5  -7  11
 94 4  -5  -7 -11  17
 95 3  -5  -7  13
 96 2  11  -5
 97 3   5  -7  11
 98 4   5  19  71 -73
 99 4   2  -5  -7  13
100 3   2  -5  11
101 4  -2   3  -5  11
102 ?
103 ?
104 4   3  -5  -7  13
105 3   3  -5  11
106 4   3   5  -7  11
107 4  -2  -3  -7  13
108 3  -2  -3  11
109 4   2   3  -5  11
110 4  -3  -7 -11  17
111 3  -3  -7  13
112 2  11  -3
113 ?
114 ?
115 4   2  -3  -7  13
116 3   2  -3  11
117 2  11  -2
118 4  -5  -7 -13  19
119 3  -7 -11  17
120 2  13  -7
121 1  11
122 4   5   7 -11  13
123 4   2  -7  17 -11
124 3   2  -7  13
125 2  11   2
126 3  -2   3  11
127 ?
128 4   3  -7  17 -11
129 3   3  -7  13
130 2  11   3
131 4  -2  -3  -5  13
132 ?
133 4  -2  -3   5  11
134 3   2   3  11
135 3  -3  -5  13
136 4  -3  -5   7  11
137 3  -3   5  11
138 ?
139 4   2  -3  -5  13
140 3  -2  -5  13
141 4   2  -3   5  11
142 3  -2   5  11
143 3  -5 -11  17
144 2  13  -5
145 3  -5   7  11
146 2  11   5
147 4   2  -5 -11  17
148 3   2  -5  13
149 4  -2   3  -5  13
150 3   2   5  11
151 4  -2   3   5  11
152 4   3  -5 -11  17
153 3   3  -5  13
154 4   3  -5   7  11
155 3   3   5  11
156 3  -2  -3  13
157 4   2   3  -5  13
158 4  -3  -5 -13  19
159 3  -3 -11  17
160 2  13  -3
161 3  -3   7  11
162 ?
163 4   2  -3 -11  17
164 3   2  -3  13
165 2  13  -2
166 3  -2   7  11
167 3  -5 -13  19
168 2  17 -11
169 1  13
170 2  11   7
171 4   2  -5  19 -13
172 3   2 -11  17
173 2  13   2
174 3   2   7  11
175 4  -2   3   7  11
176 4   3  -5  19 -13
177 3   3 -11  17
178 2  13   3
179 3   3   7  11
180 ?
181 4  -2  -3   5  13
182 3   2   3  13
183 3  -3 -13  19
184 4  -3  -5   7  13
185 3  -3   5  13
186 4  -3   5   7  11
187 4   2  -3 -13  19
188 3  -2 -13  19
189 4   2  -3   5  13
190 3  -2   5  13
191 3  -7 -11  19
192 2  19 -13
193 3  -5   7  13
194 2  13   5
195 3   5   7  11
196 3   2 -13  19
197 4  -2   3 -13  19
198 3   2   5  13
199 3   2   5   7
200 4   3  -7  19 -11

Fortran program:

C Representation of n by sum of distinct prime squares
C with minimum number of terms
C
C Hugo Pfoertner http://www.pfoertner.org
C
C Oct 22 2003 Initial version
C
      implicit integer (a-z)
      parameter (m=200,mp=200)
      dimension p(mp),a(0:m,5),c(0:m),s(mp)
      do 5 i = 0, m
      c(i)=0
      do 6 k = 1, 5
6     a(i,k)=0
5     continue
c create primes
      p(1)=2
      s(1)=4
      c(4)=1
      a(4,1)=2
      p(2)=3
      s(2)=9
      c(9)=1
      a(9,1)=3
      p(3)=5
      s(3)=25
      c(25)=1
      a(25,1)=5
      p(4)=7
      s(4)=49
      c(49)=1
      a(49,1)=7
      l = 4
      do 10 i = 11, 2000000001, 2
      if ( isprim(i) ) then
      l = l + 1
      if ( l .gt. mp ) goto 11
      p(l) = i
      s(l) = i*i
      if ( s(l) .le. m ) then
        c(s(l)) = 1
        a(s(l),1) = p(l)
      endif
      endif
10    continue
11    continue
C
C Two primes
      do 200 i = 2, 15
C Sum
      do 210 j = 1, i-1
      sum = s(i) + s(j)
      if ( sum .gt. m ) goto 211
      if ( c(sum) .eq. 0 ) then
        c(sum) = 2
        a(sum,1) = p(i)
        a(sum,2) = p(j)
      endif
210   continue
211   continue
200   continue
C
C Difference
      do 250 i = 2, mp
      if ( p(i) .gt. m/2+1 ) goto 251
      do 260 j = i-1, 1, -1
      sum = s(i) - s(j)
      if ( sum .gt. m ) goto 261
      if ( c(sum) .eq. 0 ) then
        c(sum) = 2
        a(sum,1) = p(i)
        a(sum,2) = -p(j)
      endif
260   continue
261   continue
250   continue
251   continue
C
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
C Three primes
C Sum
      do 310 i = 1, 15
      do 320 j = 1, 15
      if ( j .eq. i ) goto 320
      sij = s(i) + s(j)
      if ( sij .gt. m ) goto 321 
      do 330 k = 1, 15
      if ( k.eq.j ) goto 330
      if ( k.eq.i ) goto 330
      sum = sij + s(k)
      if ( sum .gt. m ) goto 331
      if ( c(sum) .eq. 0 ) then
        c(sum) = 3
        a(sum,1)=p(i)
        a(sum,2)=p(j)
        a(sum,3)=p(k)
      endif
330   continue 
331   continue
320   continue
321   continue
310   continue
C Differences
      do 340 i = 1, mp
      do 350 j = 1, mp
      if ( j .eq. i ) goto 350
      do 360 k = 1, mp
      if ( k .eq. i ) goto 360
      if ( k .eq. j ) goto 360
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
      sum = s(i) + s(j) - s(k)
      if ( abs(sum) .gt. m ) goto 361
      if ( sum .ge. 0 ) then
        if ( c(sum) .eq. 0 ) then
          c(sum) = 3
          a(sum,1)=p(i)
          a(sum,2)=p(j)
          a(sum,3)=-p(k)
        endif
      else
        if ( c(-sum) .eq. 0 ) then
          c(-sum) = 3
          a(-sum,1)=-p(i)
          a(-sum,2)=-p(j)
          a(-sum,3)=p(k)
        endif
      endif
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
361   continue
      sum = s(i) - s(j) - s(k)
      if ( abs(sum) .gt. m ) goto 362
      if ( sum .ge. 0 ) then
        if ( c(sum) .eq. 0 ) then
          c(sum) = 3
          a(sum,1)=p(i)
          a(sum,2)=-p(j)
          a(sum,3)=-p(k)
        endif
      else
        if ( c(-sum) .eq. 0 ) then
          c(-sum) = 3
          a(-sum,1)=-p(i)
          a(-sum,2)=p(j)
          a(-sum,3)=p(k)
        endif
      endif
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
362   continue
      sum = s(i) - s(j) + s(k)
      if ( abs(sum) .gt. m ) goto 360
      if ( sum .ge. 0 ) then
        if ( c(sum) .eq. 0 ) then
          c(sum) = 3
          a(sum,1)=p(i)
          a(sum,2)=-p(j)
          a(sum,3)=p(k)
        endif
      else
        if ( c(-sum) .eq. 0 ) then
          c(-sum) = 3
          a(-sum,1)=-p(i)
          a(-sum,2)=p(j)
          a(-sum,3)=-p(k)
        endif
      endif
360   continue
350   continue
340   continue
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
C Four primes
C Sum
      do 410 i = 1, 15
      do 420 j = 1, 15
      if ( j .eq. i ) goto 420
      sij = s(i) + s(j)
      if ( sij .gt. m ) goto 421 
      do 430 k = 1, 15
      if ( k.eq.j ) goto 430
      if ( k.eq.i ) goto 430
      sijk = sij + s(k)
      if ( sijk .gt. m ) goto 431
      do 440 l = 1, 15
      if ( l.eq.k ) goto 440
      if ( l.eq.j ) goto 440
      if ( l.eq.i ) goto 440
      sum = sijk + s(l)
      if ( sum .gt. m ) goto 441
      if ( c(sum) .eq. 0 ) then
        c(sum) = 3
        a(sum,1)=p(i)
        a(sum,2)=p(j)
        a(sum,3)=p(k)
        a(sum,4)=p(l)
        write (*,*) 4, sum, (a(sum,ii),ii=1,4)
      endif
440   continue 
441   continue 
430   continue 
431   continue
420   continue
421   continue
410   continue
C Differences
      do 450 i = 1, mp
      do 460 j = 1, mp
      if ( j .eq. i ) goto 460
      do 470 k = 1, mp
      if ( k .eq. i ) goto 470
      if ( k .eq. j ) goto 470
      do 480 l = 1, mp
      if ( l .eq. i ) goto 480
      if ( l .eq. j ) goto 480
      if ( l .eq. k ) goto 480
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
      sum = s(i) + s(j) + s(k) - s(l)
      if ( abs(sum) .gt. m ) goto 481
      if ( sum .ge. 0 ) then
        if ( c(sum) .eq. 0 ) then
          c(sum) = 4
          a(sum,1)=p(i)
          a(sum,2)=p(j)
          a(sum,3)=p(k)
          a(sum,4)=-p(l)
        write (*,*) 4, sum, (a(sum,ii),ii=1,4)
        endif
      else
        if ( c(-sum) .eq. 0 ) then
          c(-sum) = 4
          a(-sum,1)=-p(i)
          a(-sum,2)=-p(j)
          a(-sum,3)=-p(k)
          a(-sum,4)=p(l)
        write (*,*) 4, -sum, (a(-sum,ii),ii=1,4)
        endif
      endif
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
481   continue
      sum = s(i) + s(j) - s(k) + s(l)
      if ( abs(sum) .gt. m ) goto 482
      if ( sum .ge. 0 ) then
        if ( c(sum) .eq. 0 ) then
          c(sum) = 4
          a(sum,1)=p(i)
          a(sum,2)=p(j)
          a(sum,3)=-p(k)
          a(sum,4)=p(l)
        write (*,*) 4, sum, (a(sum,ii),ii=1,4)
        endif
      else
        if ( c(-sum) .eq. 0 ) then
          c(-sum) = 4
          a(-sum,1)=-p(i)
          a(-sum,2)=-p(j)
          a(-sum,3)=p(k)
          a(-sum,4)=-p(l)
        write (*,*) 4, -sum, (a(-sum,ii),ii=1,4)
        endif
      endif
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
482   continue
      sum = s(i) - s(j) + s(k) + s(l)
      if ( abs(sum) .gt. m ) goto 483
      if ( sum .ge. 0 ) then
        if ( c(sum) .eq. 0 ) then
          c(sum) = 4
          a(sum,1)=p(i)
          a(sum,2)=-p(j)
          a(sum,3)=p(k)
          a(sum,4)=p(l)
        write (*,*) 4, sum, (a(sum,ii),ii=1,4)
        endif
      else
        if ( c(-sum) .eq. 0 ) then
          c(-sum) = 4
          a(-sum,1)=-p(i)
          a(-sum,2)=p(j)
          a(-sum,3)=-p(k)
          a(-sum,4)=-p(l)
        write (*,*) 4, -sum, (a(-sum,ii),ii=1,4)
        endif
      endif
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
483   continue
      sum = - s(i) + s(j) + s(k) + s(l)
      if ( abs(sum) .gt. m ) goto 484
      if ( sum .ge. 0 ) then
        if ( c(sum) .eq. 0 ) then
          c(sum) = 4
          a(sum,1)=-p(i)
          a(sum,2)=p(j)
          a(sum,3)=p(k)
          a(sum,4)=p(l)
        write (*,*) 4, sum, (a(sum,ii),ii=1,4)
        endif
      else
        if ( c(-sum) .eq. 0 ) then
          c(-sum) = 4
          a(-sum,1)=p(i)
          a(-sum,2)=-p(j)
          a(-sum,3)=-p(k)
          a(-sum,4)=-p(l)
        write (*,*) 4, -sum, (a(-sum,ii),ii=1,4)
        endif
      endif
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
484   continue
      sum = s(i) + s(j) - s(k) - s(l)
      if ( abs(sum) .gt. m ) goto 485
      if ( sum .ge. 0 ) then
        if ( c(sum) .eq. 0 ) then
          c(sum) = 4
          a(sum,1)=p(i)
          a(sum,2)=p(j)
          a(sum,3)=-p(k)
          a(sum,4)=-p(l)
        write (*,*) 4, sum, (a(sum,ii),ii=1,4)
        endif
      else
        if ( c(-sum) .eq. 0 ) then
          c(-sum) = 4
          a(-sum,1)=-p(i)
          a(-sum,2)=-p(j)
          a(-sum,3)=p(k)
          a(-sum,4)=p(l)
        write (*,*) 4, -sum, (a(-sum,ii),ii=1,4)
        endif
      endif
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
485   continue
      sum = s(i) - s(j) + s(k) - s(l)
      if ( abs(sum) .gt. m ) goto 480
      if ( sum .ge. 0 ) then
        if ( c(sum) .eq. 0 ) then
          c(sum) = 4
          a(sum,1)=p(i)
          a(sum,2)=-p(j)
          a(sum,3)=p(k)
          a(sum,4)=-p(l)
        write (*,*) 4, sum, (a(sum,ii),ii=1,4)
        endif
      else
        if ( c(-sum) .eq. 0 ) then
          c(-sum) = 4
          a(-sum,1)=-p(i)
          a(-sum,2)=p(j)
          a(-sum,3)=-p(k)
          a(-sum,4)=p(l)
        write (*,*) 4, -sum, (a(-sum,ii),ii=1,4)
        endif
      endif
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
486   continue
      sum = s(i) - s(j) - s(k) + s(l)
      if ( abs(sum) .gt. m ) goto 480
      if ( sum .ge. 0 ) then
        if ( c(sum) .eq. 0 ) then
          c(sum) = 4
          a(sum,1)=p(i)
          a(sum,2)=-p(j)
          a(sum,3)=-p(k)
          a(sum,4)=p(l)
        write (*,*) 4, sum, (a(sum,ii),ii=1,4)
        endif
      else
        if ( c(-sum) .eq. 0 ) then
          c(-sum) = 4
          a(-sum,1)=-p(i)
          a(-sum,2)=p(j)
          a(-sum,3)=p(k)
          a(-sum,4)=-p(l)
        write (*,*) 4, -sum, (a(-sum,ii),ii=1,4)
        endif
      endif
480   continue
470   continue
460   continue
450   continue
C...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
      do 900 i = 0, m
      if ( c(i) .ne. 0 ) then
        write (*,1000) i, c(i), (a(i,k),k=1,c(i))
1000    format (i4, i2, 4i4)
      else
        write (*,1001) i
1001    format (i4, ' ?') 
      endif
900   continue
      end