Block #663,560

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/5/2014, 9:08:19 AM · Difficulty 10.9577 · 6,144,544 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

1a949124552028e523006cba730ff763222bc97b5dee6cb300c8ce5550348dd0

View on Chainz ↗

Height

#663,560

Difficulty

10.957678

Transactions

Size

886 B

Version

Bits

0af52a5c

Nonce

217,745,241

Timestamp

8/5/2014, 9:08:19 AM

Confirmations

6,144,544

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4cc73b576c09169eb0d79d21cb9809ef05c1ab6bc16a508bd9d398448dc93b65

Transactions (4)

Coinbase32c77a3f362ae4…9b5770d50574e0

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

5c4441fe1b5b98…18063bae534643

1 in → 2 out794.7899 XPM226 B

AVJsBroh…JzPrDiRN ALtsYLdB…g7K71kH3

f6b460df90d1ea…fbeecda13f289e

1 in → 2 out7.7672 XPM226 B

AcKerPva…qeeuPChG Aakfw97b…t9B8PW7f

9c7df91f28e62e…e8938a2e3f25de

1 in → 2 out1.2367 XPM226 B

AcQfYBHC…1CTjrPZw AQYh3Vj9…jwkpgczw

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.225 × 10⁹⁸(99-digit number)

22250107738366713014…55080604020331315199

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.225 × 10⁹⁸(99-digit number)

22250107738366713014…55080604020331315199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.225 × 10⁹⁸(99-digit number)

22250107738366713014…55080604020331315201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.450 × 10⁹⁸(99-digit number)

44500215476733426028…10161208040662630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.450 × 10⁹⁸(99-digit number)

44500215476733426028…10161208040662630401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.900 × 10⁹⁸(99-digit number)

89000430953466852057…20322416081325260799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.900 × 10⁹⁸(99-digit number)

89000430953466852057…20322416081325260801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.780 × 10⁹⁹(100-digit number)

17800086190693370411…40644832162650521599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.780 × 10⁹⁹(100-digit number)

17800086190693370411…40644832162650521601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.560 × 10⁹⁹(100-digit number)

35600172381386740823…81289664325301043199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.560 × 10⁹⁹(100-digit number)

35600172381386740823…81289664325301043201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #663,560

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