This is a fairly lengthy reply to the postings of Jens and Paul from
last April. Because of the length of the documentation, I will start
with a summary of my conclusions. I was using the development
version 20050215 of Winpfgw to attempt verification and extension of
some of the findings on Payam Samidoost's dual Sierpinski page:
http://sierpinski.insider.com/dual . I often ran into error messages
of the form:
2^1127+28433 ERROR DURING PROCESSING! (0.0021s+0.0093s)
However, for this particular sequence 2^n+28433, I ran up to
n<1000000 without any further error messages. (I used a sieve file
created by NewPGen which started at n=1000.) I also did not generate
any errors for the sequences 2^n+37967 for n<311,000 and for
2^n+41693 (currently near n=791,000 and stil running.) By the way, I
stopped the 37967 sequence because of the discovery of the prp
2^308809+37967. However, I encountered quite a number of errors in
the sequences for k=40291, 8543, and 2131. The errors for 40291 and
8543 generally appear to be caused by using an insufficiently large
FFT size. That is, the errors seem to start near the end of one FFT
range and stop when a new FFT size is adopted. For 40291, the last
errors occurred at n=152728 and no more errors occurred for
n<500,000, my current search bound. For 8543, I originally ran tests
on a Pentium-4 1600 MHz system but then reran some tests on an Athlon
1400 MHz system, and the results below are quite informative.
However, errors have persisted on 8543 to fairly high n values unlike
the cases for 40291 and 28433. On the other hand, errors on 2131 are
all over the map, and I am still trying to make sense of them. I
pose two key questions:

1) Is the 24.9 FFT version working properly on numbers of the form
k*2^n+/-c where c is greater than 1? It may be of interest here that
although Colin Percival's original paper treated k and c somewhat
symmetrically, George has adopted an implementation which differs in
the details between the treatment of k and c, so it is entirely
possible that his code may work perfectly on the numbers investigated
in the Sierpinski and Riesel problems but might break down on certain
cases where c>1.

2) Is the -a1 flag working properly? As seen below, I ran some tests
with the -a1 flag set, and the timings do not convince me that a
larger FFT size is actually being used. Although the original poster
was using a previous version of pfgw, I would like to raise the
possibility that he might have been seeing effects of two separate,
rather than one, problem.

So here is the lengthy part, starting with some data on 8543 run on
the older Pentium-4:

2^1119+8543 is composite: RES64: 9ACCB7B2CB7A5128 (0.0175s+0.0006s)
2^1143+8543 is composite: RES64: 39EBA08072905433 (0.0075s+0.0008s)
2^1647+8543 is composite: RES64: 8AB5BFB16DB089FF (0.0155s+0.0006s)
2^1839+8543 is composite: RES64: 5CEA8B0397D112A9 (0.0184s+0.0006s)
2^1863+8543 is composite: RES64: 438D6761AB97099C (0.0183s+0.0006s)
2^1935+8543 is composite: RES64: 437902A226091EEA (0.0189s+0.0006s)
2^2487+8543 is composite: RES64: E86837A3F74DDA98 (0.0273s+0.0006s)
2^3447+8543 is composite: RES64: 7FB8D74843DC8003 (0.0456s+0.0006s)
2^3495+8543 is composite: RES64: E71B7E72D8632F76 (0.0456s+0.0006s)
2^3855+8543 is composite: RES64: 9F00B34C343A6B26 (0.0648s+0.0006s)
2^3999+8543 is composite: RES64: CAD4163B2894EE55 (0.0610s+0.0007s)
2^4239+8543 is composite: RES64: 29B6E40CBD3E17BB (0.0633s+0.0007s)
2^5367+8543 is composite: RES64: FDECCDC3E51FCA24 (0.1022s+0.0007s)
2^6543+8543 is composite: RES64: BB65CEED2F5716BF (0.1634s+0.0007s)
2^6687+8543 is composite: RES64: 1F0B8A8A9D6820D1 (0.1656s+0.0007s)
2^7263+8543 is composite: RES64: 37EB86628EB9DFF2 (0.2266s+0.0007s)
2^7695+8543 is composite: RES64: 3383B15EC5BA2264 (0.2348s+0.0009s)
2^8055+8543 is composite: RES64: 863F03FA98370902 (0.2458s+0.0007s)
2^8247+8543 is composite: RES64: 9CFA705B7D1B9B95 (0.2442s+0.0007s)
2^8319+8543 is composite: RES64: DB4C6C96E0521D96 (0.2514s+0.0008s)
2^8823+8543 is composite: RES64: 38CFDE4F0ED4778C (0.2609s+0.0006s)
2^9399+8543 is composite: RES64: 6AE266DA7E846F37 (0.3399s+0.0048s)
2^9543+8543 is composite: RES64: 099B1C368A033CD8 (0.3549s+0.0007s)
2^9615+8543 is composite: RES64: DBC9DB40E6435945 (0.3595s+0.0006s)
2^10407+8543 is composite: RES64: 7ABCAC938D4EBE25 (0.4114s+0.0009s)
2^11223+8543 is composite: RES64: A5FDA05D8E658D93 (0.4445s+0.0007s)
2^11367+8543 is composite: RES64: CA131ADAA8AF4CE6 (0.4488s+0.0007s)
2^11559+8543 is composite: RES64: 3B7BF97E9B54B833 (0.4429s+0.0064s)
2^12015+8543 ERROR DURING PROCESSING! (0.4408s+0.0007s)
2^12087+8543 ERROR DURING PROCESSING! (0.4465s+0.0067s)
2^12135+8543 ERROR DURING PROCESSING! (0.0424s+0.0057s)
2^12447+8543 is composite: RES64: ADED7C62F65BA9EF (0.6293s+0.0062s)
2^12807+8543 is composite: RES64: F0E86D7FA0A82DB6 (0.6499s+0.0007s)
2^13143+8543 is composite: RES64: E16754CF2089A937 (0.6636s+0.0063s)
2^13719+8543 is composite: RES64: BAD3F9E17685E92E (0.6879s+0.0007s)
2^13863+8543 is composite: RES64: AB584D0FD68B703D (0.7030s+0.0009s)
2^14367+8543 is composite: RES64: DE39EFF84C14BF73 (0.8778s+0.0007s)
2^15039+8543 is composite: RES64: E83EB62A8EA6D65E (1.2001s+0.0080s)
2^15327+8543 is composite: RES64: 8CD79699B40D016F (0.9383s+0.0009s)
2^15447+8543 is composite: RES64: 50D8E762C62E6BE0 (0.9428s+0.0007s)
2^15903+8543 is composite: RES64: 5828D627C7083091 (0.9722s+0.0081s)
2^17847+8543 ERROR DURING PROCESSING! (0.0781s+0.0007s)
2^18615+8543 is composite: RES64: ABE1C38054FBBC24 (1.4619s+0.0076s)
2^18999+8543 is composite: RES64: 1EE38C35C1CF86B1 (1.5074s+0.0074s)
2^20343+8543 is composite: RES64: A89A1F6DC950D85C (1.6140s+0.0009s)
2^20799+8543 is composite: RES64: 00356A8911650748 (1.6425s+0.0092s)
2^20943+8543 is composite: RES64: 9FC59E3377F88266 (1.6580s+0.0009s)
2^21927+8543 is composite: RES64: 8888353F0C4B117E (1.7418s+0.0100s)
2^22503+8543 is composite: RES64: EB6630D9DA7C7C3D (1.6978s+0.0007s)
2^22599+8543 is composite: RES64: 171670E47F407D24 (1.7146s+0.0091s)
2^22719+8543 is composite: RES64: 4D66A66F2A767A0D (1.7011s+0.0007s)
2^23007+8543 is composite: RES64: 0D50F9AEF8EA8E75 (1.7313s+0.0092s)
2^24039+8543 ERROR DURING PROCESSING! (0.0853s+0.0049s)
2^24183+8543 is composite: RES64: C41D60471C0B23C4 (2.6215s+0.0097s)
2^24447+8543 is composite: RES64: 5D73EF67731913C9 (2.6288s+0.0008s)
2^25119+8543 is composite: RES64: 6D698FC81BDD6D2F (2.7244s+0.0007s)
2^25167+8543 is composite: RES64: 22C757822BFA23B0 (2.6982s+0.0007s)
2^25239+8543 is composite: RES64: 52D489BB6A40DA45 (2.7336s+0.0097s)
2^25455+8543 is composite: RES64: B54B691120EF1497 (2.7242s+0.0097s)
2^25623+8543 is composite: RES64: 31CBA29A622B96E5 (2.7698s+0.0097s)
2^26343+8543 is composite: RES64: AAF5FDC3DC8BF396 (2.9918s+0.0100s)
2^26535+8543 is composite: RES64: 89A2F015E7AB8BC2 (3.0138s+0.0099s)
2^27183+8543 is composite: RES64: 730B870EE4A40D44 (3.2025s+0.0030s)
2^27255+8543 is composite: RES64: CA7512CACAF1DA19 (3.4612s+0.0030s)
2^27327+8543 is composite: RES64: 2430569B2EC6A005 (2.9461s+0.0030s)
2^28647+8543 is composite: RES64: F949E54461703301 (4.5131s+0.0033s)
2^28767+8543 is composite: RES64: 6432CA71DCF45BE7 (4.0013s+0.0010s)
2^28983+8543 is composite: RES64: 7807202771E2CDCD (4.0464s+0.0029s)
2^29415+8543 is composite: RES64: 1D0A20328B7AA006 (4.3937s+0.0009s)
2^29583+8543 is composite: RES64: 7C4FFB82F78844E5 (4.0083s+0.0046s)
2^29655+8543 is composite: RES64: 03A1C940A1D970FF (4.4868s+0.0069s)
2^29727+8543 is composite: RES64: 160A44FD71B2AE4A (4.2780s+0.0010s)
2^30375+8543 is composite: RES64: 54F7D7C588529ABC (4.0221s+0.0031s)
2^30447+8543 is composite: RES64: 6BF600FDE436102C (4.4325s+0.0008s)
2^30735+8543 is composite: RES64: EFA23865DC1FB8BB (4.6470s+0.0010s)
2^31023+8543 is composite: RES64: 0B45A4639F3A01F3 (4.4167s+0.0008s)
2^31095+8543 is composite: RES64: BED26F720848CF40 (4.4979s+0.0011s)
2^31455+8543 is composite: RES64: 5A8C425E2868039F (4.1936s+0.0047s)
2^31887+8543 is composite: RES64: EC069F6A11CCA197 (4.4413s+0.0010s)
2^32295+8543 is composite: RES64: 73766BDE60B6621E (4.9837s+0.0030s)
2^32895+8543 is composite: RES64: 9558B9C3C0DDDB17 (4.3278s+0.0010s)
2^33039+8543 is composite: RES64: A39FEDE3632E646C (4.4022s+0.0008s)
2^33735+8543 is composite: RES64: F47FCA51A7268BF1 (4.2220s+0.0010s)
2^33903+8543 is composite: RES64: 2D425E1B2EF13958 (4.3979s+0.0046s)
2^34383+8543 ERROR DURING PROCESSING! (0.1372s+0.0049s)
2^34623+8543 ERROR DURING PROCESSING! (4.4251s+0.0031s)
2^36207+8543 is composite: RES64: A6939DEAD4A60331 (6.0875s+0.0028s)
2^36423+8543 is composite: RES64: 1B61A14EF263DEBC (6.2049s+0.0008s)
2^36495+8543 is composite: RES64: D123DCA2AA7E753B (6.8151s+0.0008s)
2^36567+8543 is composite: RES64: B00612DC956D08DF (6.3179s+0.0010s)
2^36999+8543 is composite: RES64: 20CCF8D51E1F0062 (6.1868s+0.0010s)
2^37287+8543 is composite: RES64: 97BFFD4DD0793899 (6.5919s+0.0010s)
2^38055+8543 is composite: RES64: B4AAA110FDA2259B (7.2386s+0.0030s)
2^38127+8543 is composite: RES64: BA5EA0C3BD517910 (7.2254s+0.0008s)
2^38343+8543 is composite: RES64: E24FBCE19F924A34 (6.4329s+0.0010s)
2^38655+8543 is composite: RES64: AAA0457B5B6A577D (6.6391s+0.0030s)
2^38799+8543 is composite: RES64: 900C0BF9FE2D38E1 (6.4948s+0.0030s)
2^38943+8543 is composite: RES64: D3B4CC500C21AC55 (6.9080s+0.0044s)
2^39495+8543 is composite: RES64: EF10FB53917D46C7 (6.7363s+0.0011s)
2^39639+8543 is composite: RES64: 55BB98795010F60B (6.8867s+0.0011s)
2^39735+8543 is composite: RES64: D4D0AC2FC245D3C7 (6.7739s+0.0033s)
2^39999+8543 is composite: RES64: B72545D1D74E7943 (7.0168s+0.0008s)
2^40143+8543 is composite: RES64: BCD6437B02B5BB1B (6.8692s+0.0048s)
2^40455+8543 is composite: RES64: 01E6814C2C289CE3 (7.1693s+0.0030s)
2^40527+8543 is composite: RES64: E2FFDDF2F10DC72E (6.9708s+0.0008s)
2^40959+8543 is composite: RES64: 4F8D95C873B17AE6 (7.2917s+0.0011s)
2^41439+8543 is composite: RES64: 3FF6C0EA0DDD5454 (7.1064s+0.0030s)
2^41535+8543 is composite: RES64: 8061B6F4B2701E70 (7.3187s+0.0046s)
2^43047+8543 is composite: RES64: 3ADD8578E7897AEE (7.3154s+0.0030s)
2^44127+8543 is composite: RES64: 89D6B564D652B13F (7.6724s+0.0008s)
2^44487+8543 is composite: RES64: DCD422261D28C9FB (7.7881s+0.0030s)
2^44607+8543 is composite: RES64: 954F05EC89CCCD40 (7.5518s+0.0009s)
2^44703+8543 is composite: RES64: 305828D9F4568D14 (7.8423s+0.0067s)
2^44823+8543 is composite: RES64: 56AA8C7D4A0A8E9D (7.5027s+0.0010s)
2^45039+8543 is composite: RES64: C420613BDEC1093D (7.7151s+0.0030s)
2^45207+8543 is composite: RES64: EEC670B136ECF39E (7.6809s+0.0011s)
2^45567+8543 ERROR DURING PROCESSING! (8.0773s+0.0044s)
2^46287+8543 ERROR DURING PROCESSING! (0.1714s+0.0029s)
2^46575+8543 ERROR DURING PROCESSING! (0.1775s+0.0030s)
2^47055+8543 ERROR DURING PROCESSING! (0.1712s+0.0030s)
2^47127+8543 ERROR DURING PROCESSING! (0.1715s+0.0030s)
2^47367+8543 is composite: RES64: E3AB9F0E5E212DB4 (11.3251s+0.0029s)
2^47559+8543 is composite: RES64: E6DCA1C3A3F82EE5 (11.1331s+0.0011s)
2^47583+8543 is composite: RES64: 8F2B97FD3A178EE7 (11.0151s+0.0045s)
2^48063+8543 is composite: RES64: C975C66C1486F7B5 (11.1256s+0.0030s)
2^48423+8543 is composite: RES64: AD224BE6B65F3AB0 (11.3182s+0.0010s)
2^48519+8543 is composite: RES64: 7A7146503838F0DF (11.2466s+0.0046s)
2^48639+8543 is composite: RES64: 1E3A47CAC093F18B (11.0042s+0.0008s)
2^48735+8543 is composite: RES64: 751E3B31F9834D0E (11.2166s+0.0011s)
2^49095+8543 is composite: RES64: 2F664986EC1D1FE6 (11.3003s+0.0047s)
2^49239+8543 is composite: RES64: 6C64EC5557065334 (11.2018s+0.0008s)
2^49383+8543 is composite: RES64: D3CF417E065AEA81 (11.3106s+0.0031s)
2^49575+8543 is composite: RES64: EA14AB5E61FA25E7 (11.4465s+0.0067s)
2^49647+8543 is composite: RES64: D809AAF9679F1CE9 (11.4151s+0.0010s)
2^49719+8543 is composite: RES64: 5735291D209E2649 (11.5797s+0.0011s)

Now the same tests on the Athlon system:

2^1119+8543 is composite: RES64: 9ACCB7B2CB7A5128 (0.0066s+0.0002s)
2^1143+8543 is composite: RES64: 39EBA08072905433 (0.0065s+0.0003s)
2^1647+8543 is composite: RES64: 8AB5BFB16DB089FF (4.9794s+0.0002s)
2^1839+8543 is composite: RES64: 5CEA8B0397D112A9 (0.0164s+0.0005s)
2^1863+8543 is composite: RES64: 438D6761AB97099C (0.0191s+0.0003s)
2^1935+8543 is composite: RES64: 437902A226091EEA (0.0196s+0.0002s)
2^2487+8543 is composite: RES64: E86837A3F74DDA98 (0.0304s+0.0002s)
2^3447+8543 is composite: RES64: 7FB8D74843DC8003 (0.0551s+0.0002s)
2^3495+8543 is composite: RES64: E71B7E72D8632F76 (4.8683s+0.0003s)
2^3855+8543 is composite: RES64: 9F00B34C343A6B26 (0.0720s+0.0005s)
2^3999+8543 is composite: RES64: CAD4163B2894EE55 (0.0741s+0.0003s)
2^4239+8543 is composite: RES64: 29B6E40CBD3E17BB (4.8910s+0.0004s)
2^5367+8543 is composite: RES64: FDECCDC3E51FCA24 (0.1282s+0.0004s)
2^6543+8543 is composite: RES64: BB65CEED2F5716BF (9.8390s+0.0003s)
2^6687+8543 is composite: RES64: 1F0B8A8A9D6820D1 (5.1095s+0.0032s)
2^7263+8543 is composite: RES64: 37EB86628EB9DFF2 (9.0044s+0.0003s)
2^7695+8543 is composite: RES64: 3383B15EC5BA2264 (0.2995s+0.0068s)
2^8055+8543 is composite: RES64: 863F03FA98370902 (0.3118s+0.0003s)
2^8247+8543 is composite: RES64: 9CFA705B7D1B9B95 (0.3214s+0.0003s)
2^8319+8543 is composite: RES64: DB4C6C96E0521D96 (0.3238s+0.0003s)
2^8823+8543 is composite: RES64: 38CFDE4F0ED4778C (0.3248s+0.0004s)
2^9399+8543 is composite: RES64: 61ED7EB482988FCE (0.3461s+0.0003s)
2^9543+8543 is composite: RES64: 099B1C368A033CD8 (0.4887s+0.0003s)
2^9615+8543 is composite: RES64: DBC9DB40E6435945 (0.4583s+0.0065s)
2^10407+8543 is composite: RES64: 7ABCAC938D4EBE25 (0.5244s+0.0003s)
2^11223+8543 is composite: RES64: A5FDA05D8E658D93 (0.5625s+0.0004s)
2^11367+8543 is composite: RES64: CA131ADAA8AF4CE6 (0.5768s+0.0003s)
2^11559+8543 is composite: RES64: 3B7BF97E9B54B833 (0.6139s+0.0062s)
2^12015+8543 is composite: RES64: A5F29AECA630CD6B (0.5715s+0.0003s)
2^12087+8543 is composite: RES64: 9680B57606578932 (0.6033s+0.0004s)
2^12135+8543 is composite: RES64: F601FB9D4CB75B2A (0.5747s+0.0004s)
2^12447+8543 ERROR DURING PROCESSING! (0.0221s+0.0066s)
2^12807+8543 is composite: RES64: F0E86D7FA0A82DB6 (0.8462s+0.0062s)
2^13143+8543 is composite: RES64: E16754CF2089A937 (0.8800s+0.0003s)
2^13719+8543 is composite: RES64: BAD3F9E17685E92E (0.8997s+0.0004s)
2^13863+8543 is composite: RES64: AB584D0FD68B703D (0.9739s+0.0003s)
2^14367+8543 is composite: RES64: DE39EFF84C14BF73 (1.1513s+0.0054s)
2^15039+8543 is composite: RES64: E83EB62A8EA6D65E (1.1760s+0.0004s)
2^15327+8543 is composite: RES64: 8CD79699B40D016F (1.2249s+0.0068s)
2^15447+8543 is composite: RES64: 50D8E762C62E6BE0 (1.2659s+0.0005s)
2^15903+8543 is composite: RES64: 5828D627C7083091 (1.2393s+0.0066s)
2^17847+8543 is composite: RES64: 5D2F357139BE9759 (1.3411s+0.0004s)
2^18615+8543 is composite: RES64: ABE1C38054FBBC24 (1.9666s+0.0004s)
2^18999+8543 is composite: RES64: 1EE38C35C1CF86B1 (1.9199s+0.0066s)
2^20343+8543 is composite: RES64: A89A1F6DC950D85C (2.1164s+0.0003s)
2^20799+8543 is composite: RES64: 00356A8911650748 (2.2182s+0.0003s)
2^20943+8543 is composite: RES64: 9FC59E3377F88266 (2.1400s+0.0068s)
2^21927+8543 is composite: RES64: 8888353F0C4B117E (2.3665s+0.0066s)
2^22503+8543 is composite: RES64: EB6630D9DA7C7C3D (2.3339s+0.0003s)
2^22599+8543 is composite: RES64: 171670E47F407D24 (2.4076s+0.0034s)
2^22719+8543 is composite: RES64: 4D66A66F2A767A0D (2.3834s+0.0067s)
2^23007+8543 is composite: RES64: B30CB31FF14C22F1 (2.4468s+0.0065s)
2^24039+8543 is composite: RES64: 6D00F0BB7743A71A (2.6082s+0.0069s)
2^24183+8543 is composite: RES64: 80B336ED0969CDC8 (2.5851s+0.0003s)
2^24447+8543 is composite: RES64: 8321C82D1B529213 (2.5449s+0.0003s)
2^25119+8543 is composite: RES64: 6D698FC81BDD6D2F (3.9026s+0.0003s)
2^25167+8543 is composite: RES64: 22C757822BFA23B0 (3.8720s+0.0004s)
2^25239+8543 is composite: RES64: 52D489BB6A40DA45 (4.1804s+0.0053s)
2^25455+8543 is composite: RES64: B54B691120EF1497 (4.2103s+0.0003s)
2^25623+8543 is composite: RES64: 31CBA29A622B96E5 (3.9379s+0.0038s)
2^26343+8543 is composite: RES64: AAF5FDC3DC8BF396 (3.8721s+0.0057s)
2^26535+8543 is composite: RES64: 89A2F015E7AB8BC2 (3.8814s+0.0003s)
2^27183+8543 is composite: RES64: 730B870EE4A40D44 (4.1233s+0.0003s)
2^27255+8543 is composite: RES64: CA7512CACAF1DA19 (3.9420s+0.0056s)
2^27327+8543 is composite: RES64: 2430569B2EC6A005 (3.9807s+0.0057s)
2^28647+8543 is composite: RES64: F949E54461703301 (5.1821s+0.0004s)
2^28767+8543 is composite: RES64: 6432CA71DCF45BE7 (5.3176s+0.0003s)
2^28983+8543 is composite: RES64: 7807202771E2CDCD (5.1558s+0.0082s)
2^29415+8543 is composite: RES64: 1D0A20328B7AA006 (5.2904s+0.0004s)
2^29583+8543 is composite: RES64: 7C4FFB82F78844E5 (5.3089s+0.0003s)
2^29655+8543 is composite: RES64: 03A1C940A1D970FF (5.4213s+0.0003s)
2^29727+8543 is composite: RES64: 160A44FD71B2AE4A (5.3993s+0.0051s)
2^30375+8543 is composite: RES64: 54F7D7C588529ABC (5.4976s+0.0067s)
2^30447+8543 is composite: RES64: 6BF600FDE436102C (5.4609s+0.0035s)
2^30735+8543 is composite: RES64: EFA23865DC1FB8BB (5.5876s+0.0003s)
2^31023+8543 is composite: RES64: 0B45A4639F3A01F3 (5.6744s+0.0003s)
2^31095+8543 is composite: RES64: BED26F720848CF40 (5.5155s+0.0003s)
2^31455+8543 is composite: RES64: 5A8C425E2868039F (5.7239s+0.0056s)
2^31887+8543 is composite: RES64: EC069F6A11CCA197 (5.7181s+0.0069s)
2^32295+8543 is composite: RES64: 73766BDE60B6621E (5.9835s+0.0256s)
2^32895+8543 is composite: RES64: 9558B9C3C0DDDB17 (6.0280s+0.0064s)
2^33039+8543 is composite: RES64: A39FEDE3632E646C (6.1695s+0.0004s)
2^33735+8543 is composite: RES64: F47FCA51A7268BF1 (6.0642s+0.0044s)
2^33903+8543 is composite: RES64: 2D425E1B2EF13958 (5.9791s+0.0045s)
2^34383+8543 is composite: RES64: DAEB912E58A5C52E (6.1384s+0.0050s)
2^34623+8543 is composite: RES64: EE242D082AD05C38 (6.1187s+0.0046s)
2^36207+8543 ERROR DURING PROCESSING! (0.0656s+0.0074s)
2^36423+8543 is composite: RES64: 1B61A14EF263DEBC (8.7193s+0.0044s)
2^36495+8543 is composite: RES64: D123DCA2AA7E753B (8.3896s+0.0070s)
2^36567+8543 is composite: RES64: B00612DC956D08DF (8.4063s+0.0069s)
2^36999+8543 is composite: RES64: 20CCF8D51E1F0062 (8.7252s+0.0004s)
2^37287+8543 is composite: RES64: 97BFFD4DD0793899 (9.0229s+0.0004s)
2^38055+8543 is composite: RES64: B4AAA110FDA2259B (8.8623s+0.0035s)
2^38127+8543 is composite: RES64: BA5EA0C3BD517910 (8.8596s+0.0004s)
2^38343+8543 is composite: RES64: E24FBCE19F924A34 (8.9077s+0.0004s)
2^38655+8543 is composite: RES64: AAA0457B5B6A577D (9.0453s+0.0003s)
2^38799+8543 is composite: RES64: 900C0BF9FE2D38E1 (9.7760s+0.0034s)
2^38943+8543 is composite: RES64: D3B4CC500C21AC55 (9.1009s+0.0004s)
2^39495+8543 is composite: RES64: EF10FB53917D46C7 (10.6619s+0.0004s)
2^39639+8543 is composite: RES64: 55BB98795010F60B (10.0210s+0.0003s)
2^39735+8543 is composite: RES64: D4D0AC2FC245D3C7 (9.9225s+0.0035s)
2^39999+8543 is composite: RES64: B72545D1D74E7943 (9.7375s+0.0051s)
2^40143+8543 is composite: RES64: BCD6437B02B5BB1B (9.3346s+0.0054s)
2^40455+8543 is composite: RES64: 01E6814C2C289CE3 (9.4558s+0.0004s)
2^40527+8543 is composite: RES64: E2FFDDF2F10DC72E (9.4676s+0.0035s)
2^40959+8543 is composite: RES64: 4F8D95C873B17AE6 (9.6656s+0.0004s)
2^41439+8543 is composite: RES64: 3FF6C0EA0DDD5454 (9.7408s+0.0005s)
2^41535+8543 is composite: RES64: 8061B6F4B2701E70 (9.6974s+0.0055s)
2^43047+8543 is composite: RES64: 3ADD8578E7897AEE (10.1321s+0.0034s)
2^44127+8543 is composite: RES64: 89D6B564D652B13F (10.3678s+0.0004s)
2^44487+8543 is composite: RES64: E011AF73F67871E1 (10.3852s+0.0050s)
2^44607+8543 is composite: RES64: 6FF9014E2776ADA6 (10.5853s+0.0035s)
2^44703+8543 is composite: RES64: 18E821B5DCA44E36 (10.4063s+0.0055s)
2^44823+8543 is composite: RES64: 39004B9492B12C62 (10.4092s+0.0004s)
2^45039+8543 is composite: RES64: 026C8B07BEC5A301 (10.5621s+0.0081s)
2^45207+8543 is composite: RES64: AA3035E5EB78CA08 (11.1032s+0.0005s)
2^45567+8543 is composite: RES64: 150729FC01005DD9 (11.0445s+0.0004s)
2^46287+8543 is composite: RES64: 58AE27E30E4ED942 (11.0479s+0.0083s)
2^46575+8543 is composite: RES64: 251F6364E8CA1B15 (11.0640s+0.0007s)
2^47055+8543 ERROR DURING PROCESSING! (0.0863s+0.0004s)
2^47127+8543 ERROR DURING PROCESSING! (11.2046s+0.0050s)
2^47367+8543 ERROR DURING PROCESSING! (0.0930s+0.0074s)
2^47559+8543 ERROR DURING PROCESSING! (0.0915s+0.0046s)
2^47583+8543 ERROR DURING PROCESSING! (0.0893s+0.0046s)
2^48063+8543 ERROR DURING PROCESSING! (0.0797s+0.0046s)
2^48423+8543 ERROR DURING PROCESSING! (0.0799s+0.0049s)
2^48519+8543 ERROR DURING PROCESSING! (0.0798s+0.0046s)
2^48639+8543 is composite: RES64: 1E3A47CAC093F18B (16.5434s+0.0047s)
2^48735+8543 is composite: RES64: 751E3B31F9834D0E (16.4908s+0.0004s)
2^49095+8543 is composite: RES64: 2F664986EC1D1FE6 (16.5981s+0.0081s)
2^49239+8543 is composite: RES64: 6C64EC5557065334 (16.6547s+0.0005s)
2^49383+8543 is composite: RES64: D3CF417E065AEA81 (16.6496s+0.0082s)
2^49575+8543 is composite: RES64: EA14AB5E61FA25E7 (16.7412s+0.0005s)
2^49647+8543 is composite: RES64: D809AAF9679F1CE9 (16.7494s+0.0083s)
2^49719+8543 is composite: RES64: 5735291D209E2649 (16.8295s+0.0004s)

Note that because the Athlon has larger FFT breakpoints, that the
errors occur at slightly larger n values, but the errors always seem
to occur near a jump in FFT size. There also appear in both cases to
be erroneous residues which are not caught with the ERROR DURING
PROCESSING! messages.

This seems to be a general pattern, but it is not clear why some k
values seem to generate more errors than others. However, k=2131, as
I mentioned before, seems infested with these messages, sometimes
affecting approximately 10% of all tests, but I don't see a clear FFT
size pattern.

I reran several tests which had suspicious Pentium 4 results on the
Athlon:

2^12087+8543 is composite: RES64: 9680B57606578932 (0.5885s+0.0003s)
2^12135+8543 is composite: RES64: F601FB9D4CB75B2A (0.5742s+0.0005s)
2^17847+8543 is composite: RES64: 5D2F357139BE9759 (1.4127s+0.0005s)
2^24039+8543 is composite: RES64: 6D00F0BB7743A71A (2.5262s+0.0052s)
2^34383+8543 is composite: RES64: DAEB912E58A5C52E (6.1586s+0.0063s)
2^34623+8543 is composite: RES64: EE242D082AD05C38 (6.2084s+0.0063s)
2^45567+8543 is composite: RES64: 150729FC01005DD9 (11.7991s+0.0065s)
2^46287+8543 is composite: RES64: 58AE27E30E4ED942 (11.4373s+0.0045s)
2^46575+8543 is composite: RES64: 251F6364E8CA1B15 (11.7485s+0.0005s)
2^47055+8543 ERROR DURING PROCESSING! (11.5733s+0.0036s)
2^47127+8543 is composite: RES64: 8294454C5F3CD262 (11.8062s+0.0042s)
2^67167+8543 is composite: RES64: 331AA47C4F940772 (27.0994s+0.0004s)
2^67455+8543 is composite: RES64: F2A47ADC0E604F50 (27.6464s+0.0004s)
2^67575+8543 is composite: RES64: 2AD923F7FD0F3BE7 (26.7575s+0.0004s)
2^67743+8543 is composite: RES64: 4FC1B09629E5568B (26.7448s+0.0034s)
2^67863+8543 is composite: RES64: 55256D0CC6C01439 (26.7851s+0.0005s)
2^68007+8543 is composite: RES64: C5349EC1DD2D227B (26.8941s+0.0037s)
2^68583+8543 is composite: RES64: CD235E0FD4E93366 (27.0606s+0.0004s)
2^68967+8543 is composite: RES64: 09947D5C5EEB6A93 (27.3796s+0.0034s)
2^69015+8543 is composite: RES64: 4627548D667A860F (28.0563s+0.0004s)
2^69303+8543 is composite: RES64: 6F18BCBB5FF35D9D (28.4653s+0.0004s)
2^69735+8543 is composite: RES64: 33042572C89E4FC1 (29.2658s+0.0057s)
2^70023+8543 ERROR DURING PROCESSING! (0.0442s+0.0004s)
2^70383+8543 ERROR DURING PROCESSING! (0.0431s+0.0045s)
2^70527+8543 is composite: RES64: F503D60450244CAF (35.4997s+0.0045s)
2^70743+8543 is composite: RES64: 29642A80225A7B62 (35.3088s+0.0033s)
2^71055+8543 is composite: RES64: FCDC1A8D38898490 (34.9575s+0.0034s)
2^71487+8543 is composite: RES64: 80518CA6A920965D (35.2327s+0.0035s)
2^88335+8543 is composite: RES64: 24A744A5005FF7B1 (48.0461s+0.0036s)
2^88959+8543 is composite: RES64: C0B2CFBB211F24E3 (47.5203s+0.0095s)
2^89247+8543 is composite: RES64: 28007A364BAF961C (46.6636s+0.0004s)
2^89919+8543 is composite: RES64: 5232EB29F2DC949E (47.0354s+0.0097s)
2^91215+8543 ERROR DURING PROCESSING! (47.4396s+0.0095s)
2^91767+8543 ERROR DURING PROCESSING! (47.8167s+0.0080s)
2^91935+8543 is composite: RES64: 77C973375167F141 (47.9119s+0.0093s)
2^130023+8543 is composite: RES64: 68977B47B1D874D9
(116.4333s+0.0096s)
Resuming input file 8543errs.txt at line 38

Resuming at bit 39879
2^130719+8543 is composite: RES64: 0BCFB353AA71F5BC (81.3962s+0.0314s)
Resuming input file 8543errs.txt at line 39

2^130887+8543 is composite: RES64: 5223F4143F738DDF
(117.6123s+0.0004s)
2^131007+8543 is composite: RES64: 3A1FAAEAF10C95F3
(113.8062s+0.0079s)
2^131895+8543 is composite: RES64: 57A3937A282DD40F
(114.1536s+0.0033s)
2^132039+8543 is composite: RES64: CA8B1240E6852B30
(114.4128s+0.0034s)
2^132255+8543 is composite: RES64: 2853562425605FD7
(115.0690s+0.0033s)
2^132399+8543 is composite: RES64: 9BE56CD69F5A4BB7
(114.7508s+0.0076s)
2^132519+8543 is composite: RES64: 61CDB502B94EEE03
(114.9537s+0.0078s)
2^132687+8543 is composite: RES64: 0DF30136BA1FD7F6
(115.1233s+0.0077s)
2^132735+8543 is composite: RES64: 894546B183417827
(114.9485s+0.0074s)
2^132807+8543 is composite: RES64: 60690BBC1AE02785
(115.2156s+0.0033s)
2^132903+8543 is composite: RES64: 098C1848BC7E93F5
(115.1228s+0.0033s)
2^133167+8543 is composite: RES64: B0B0174ADEFF3B17
(115.2806s+0.0032s)
2^133887+8543 is composite: RES64: 8B76CAB94424C352
(116.1042s+0.0033s)
2^134247+8543 is composite: RES64: CDEA26375FB6892C
(116.1837s+0.0076s)
2^172695+8543 is composite: RES64: 5383E7090C6D3A3C
(203.3608s+0.0035s)
2^173007+8543 is composite: RES64: 83E5CCB12D4C31ED
(203.8346s+0.0033s)
2^173487+8543 is composite: RES64: 1F64350A01DDC469
(204.3037s+0.0033s)
2^173799+8543 is composite: RES64: 11DB1FE3F6CE75B9
(204.9196s+0.0034s)
2^173847+8543 is composite: RES64: 3C42F7758FFE100D
(204.6290s+0.0035s)
2^173919+8543 is composite: RES64: A416E165A10E9205
(204.7114s+0.0034s)
2^174135+8543 is composite: RES64: 220B65D52E52B018
(205.1239s+0.0035s)
2^174303+8543 is composite: RES64: F4B6EF3A4B1F3CCD
(215.6652s+0.0075s)
2^174663+8543 is composite: RES64: 765FFD55B6FECC00
(205.8063s+0.0079s)
2^175095+8543 is composite: RES64: 0102AF91DE2B494E
(206.3101s+0.0076s)
2^175719+8543 is composite: RES64: FE3CABC3F028956F
(203.4529s+0.0035s)
2^176823+8543 is composite: RES64: 8573712EB42F0FB2
(204.6589s+0.0036s)
2^178239+8543 is composite: RES64: 6A342F3A74BCD119
(206.4813s+0.0076s)
2^256239+8543 is composite: RES64: B74737CB4E7513CF
(479.8282s+0.0081s)
2^256383+8543 is composite: RES64: 03E37EDC9EE1E8FF
(478.5673s+0.0078s)
2^256503+8543 is composite: RES64: 4CDB56C12642D899
(479.6068s+0.0077s)
2^256863+8543 is composite: RES64: DD3F652A7E856A32
(479.2833s+0.0085s)
2^257247+8543 is composite: RES64: ACDBF6E02BCA8333
(480.8312s+0.0078s)
2^257967+8543 is composite: RES64: 3BDF59F6DAB7B746
(481.7218s+0.0077s)
2^258015+8543 is composite: RES64: C9E748DC599F3E05
(481.4841s+0.0037s)
2^258303+8543 is composite: RES64: 26B824E345591976
(504.4973s+0.0036s)
2^258327+8543 is composite: RES64: 64043F9B59120E67
(481.5428s+0.0036s)
2^258663+8543 is composite: RES64: EC9D370ECC6AA1D4
(482.4372s+0.0036s)
2^259047+8543 is composite: RES64: 139DEB04952B5C58
(483.4587s+0.0076s)
2^259095+8543 is composite: RES64: 401F3EE9BCB6E95E
(484.7420s+0.0076s)
2^259407+8543 is composite: RES64: B30C7E007B0D5A12
(483.0724s+0.0081s)
2^259887+8543 is composite: RES64: 00329C502CD2261F
(475.3531s+0.0079s)
2^259983+8543 is composite: RES64: DB2335196E26BAD2
(475.3824s+0.0079s)
2^260103+8543 ERROR DURING PROCESSING! (0.2381s+0.0075s)
2^260607+8543 is composite: RES64: 6D957DA39EE09C41
(476.5470s+0.0046s)
2^260775+8543 is composite: RES64: 9A6EA4DF5D887413
(476.3434s+0.0039s)
2^261039+8543 is composite: RES64: C4A00BD900807058
(477.7431s+0.0035s)
2^261183+8543 is composite: RES64: 9E5890BA32FD8853
(477.2612s+0.0082s)
2^261399+8543 is composite: RES64: FA55D32B6D65B713
(478.0196s+0.0076s)
2^261423+8543 is composite: RES64: E72009615D1EDD56
(477.3700s+0.0080s)
2^262359+8543 is composite: RES64: 7C1A1832FA20F0F8
(478.8335s+0.0078s)
2^262623+8543 ERROR DURING PROCESSING! (480.1843s+0.0078s)
2^340959+8543 is composite: RES64: 8213DC54B6CDDDB6
(897.7186s+0.0078s)
2^341559+8543 is composite: RES64: 8C957CC5C62511B0
(895.4308s+0.0080s)
2^341919+8543 is composite: RES64: AC3FE529A0E4BD09
(896.6870s+0.0081s)
2^342207+8543 is composite: RES64: E7C40FA74F43C80C
(902.5589s+0.0082s)
2^343047+8543 is composite: RES64: 7199C3193C9BCFD0
(899.0159s+0.0081s)
2^343215+8543 is composite: RES64: DB48B487F91E6376
(899.4960s+0.0037s)
2^343719+8543 is composite: RES64: 959289621DEE5A1E
(904.2331s+0.0078s)
2^343863+8543 is composite: RES64: B9294AB6E78393E2
(906.7754s+0.0082s)
2^343983+8543 is composite: RES64: A3074BE26AEE7085
(903.1982s+0.0079s)
2^344007+8543 is composite: RES64: 286DED8BD86A3EEC
(908.2783s+0.0080s)
2^344343+8543 is composite: RES64: 829A25443C5FEED6
(904.9632s+0.0082s)
2^344559+8543 is composite: RES64: 52658525ABDFD3AB
(1071.2060s+0.0099s)
2^345519+8543 is composite: RES64: BA09DFE12E4080EB
(1026.4191s+0.0083s)
2^346167+8543 is composite: RES64: 4EFBEA91A80C621A
(909.6016s+0.0035s)
2^346503+8543 is composite: RES64: 04C072EF5B516606
(937.7336s+0.0087s)
2^347103+8543 is composite: RES64: DAA223ED8C6186F6
(899.3469s+0.0080s)
2^347175+8543 is composite: RES64: CBBD467F331FA478
(889.9860s+0.0081s)
2^347223+8543 ERROR DURING PROCESSING! (894.1441s+0.0077s)
2^347463+8543 ERROR DURING PROCESSING! (897.4831s+0.0072s)
2^347583+8543 ERROR DURING PROCESSING! (893.6739s+0.0072s)
2^347727+8543 ERROR DURING PROCESSING! (890.0623s+0.0077s)
2^347895+8543 is composite: RES64: 9B5AEFB66FD199E9
(900.5352s+0.0077s)
2^347943+8543 is composite: RES64: A3E47B998AA739CB
(891.8989s+0.0037s)
2^348255+8543 ERROR DURING PROCESSING! (0.2163s+0.0035s)

Then I reran several tests with the -a1 flag set:

2^46287+8543 is composite: RES64: 58AE27E30E4ED942 (10.8693s+0.0003s)
2^46575+8543 is composite: RES64: 251F6364E8CA1B15 (10.6872s+0.0005s)
2^47055+8543 ERROR DURING PROCESSING! (10.8034s+0.0066s)
2^47127+8543 is composite: RES64: 8294454C5F3CD262 (11.0106s+0.0079s)
2^69735+8543 is composite: RES64: 33042572C89E4FC1 (27.2779s+0.0003s)
2^70023+8543 ERROR DURING PROCESSING! (0.0432s+0.0034s)
2^70383+8543 ERROR DURING PROCESSING! (27.4537s+0.0063s)
2^70527+8543 ERROR DURING PROCESSING! (0.0552s+0.0048s)
2^89919+8543 is composite: RES64: 5232EB29F2DC949E (49.9142s+0.0050s)
2^91215+8543 is composite: RES64: F650D4087270FEEB (48.5128s+0.0035s)
2^91767+8543 is composite: RES64: FD8B91322F9FD892 (49.1859s+0.0078s)
2^91935+8543 ERROR DURING PROCESSING! (0.0563s+0.0080s)
2^259983+8543 is composite: RES64: DB2335196E26BAD2
(485.1689s+0.0047s)
2^260103+8543 is composite: RES64: 90116453CD1B53E3
(484.8119s+0.0081s)
2^260607+8543 is composite: RES64: 6D957DA39EE09C41
(485.5523s+0.0035s)
2^262359+8543 is composite: RES64: 298B7FC9A8051632
(488.6482s+0.0036s)
2^262623+8543 is composite: RES64: BCDDDA3ED1A3A9FC
(491.4026s+0.0081s)
2^340959+8543 is composite: RES64: 8213DC54B6CDDDB6
(892.3890s+0.0037s)
2^344559+8543 is composite: RES64: 52658525ABDFD3AB
(905.8554s+0.0081s)
2^345519+8543 is composite: RES64: BA09DFE12E4080EB
(908.1915s+0.0080s)
2^346167+8543 is composite: RES64: 4EFBEA91A80C621A
(910.5305s+0.0038s)
2^346503+8543 is composite: RES64: 04C072EF5B516606
(911.4427s+0.0078s)
2^347103+8543 is composite: RES64: 018EE3A9B463A20D
(912.6328s+0.0083s)
2^347175+8543 is composite: RES64: 473ECDAF5F4F57CA
(913.8914s+0.0079s)
2^347223+8543 is composite: RES64: F5BAA8CDCF335B9F
(914.0341s+0.0081s)
2^347463+8543 is composite: RES64: FE5198684343CD8C
(915.2995s+0.0086s)
2^347583+8543 is composite: RES64: B27F1A9208FFDBA4
(915.5863s+0.0079s)
2^347727+8543 is composite: RES64: 0679A4849A110B1F
(912.6941s+0.0036s)
2^347895+8543 is composite: RES64: 7F09A4C454EA35CE
(915.4605s+0.0036s)
2^347943+8543 is composite: RES64: C520CAD2E015D887
(913.4917s+0.0036s)
2^348255+8543 is composite: RES64: 2CC8801666657B42
(916.5908s+0.0036s)

Note the very slight increase in running time, or in some cases,
actually a slight decrease. If one is using an appreciably larger
FFT size, I would expect the time to increase appreciably. Is the -
a1 flag actually doing what it is supposed to?

At any rate, I will stop here for now, but as I study the 2131 data
and run more tests, I will post again. The 2131 data has been
running on a Pentium D system, but I would like to see how much of
the flakiness can be reproduced on the Athlon system.

Phil