Block #440,859

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 5:27:51 PM · Difficulty 10.3526 · 6,384,440 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d8c15d6da569e467509c40756cdc622ef53c1d13a3e89870a1557ce2d14db08e

View on Chainz ↗

Height

#440,859

Difficulty

10.352637

Transactions

Size

1.64 KB

Version

Bits

0a5a4666

Nonce

41,825

Timestamp

3/12/2014, 5:27:51 PM

Confirmations

6,384,440

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

940a8ef52dbca42a671cd6b278a2993cceb69e587cc0dfbded54bd4907b6f43b

Transactions (4)

Coinbase53b59be9f0330f…bd395c9d55c3d6

1 in → 1 out9.3600 XPM110 B

AeKNrjNj…1NEq95Ta

40831b24981698…fa5b2b805b5056

5 in → 11 out31.6496 XPM1.00 KB

AXDxHYBt…YpciAxSr AREyVUQx…fNuPnjDA AYJq4YVd…sPb3dC2v AeKNrjNj…1NEq95Ta AUDA3a2M…mDChw1vJ

4d78d1814f14f9…a2998a1561c8ad

1 in → 2 out3.1423 XPM225 B

AZTS3grf…3mKBxi7k AdK1qvp1…2e7J62K9

1038a658fd8d92…38c9558ad99796

1 in → 2 out2.4298 XPM226 B

AHpstxpY…wwV1SAf8 ATNYqnBR…wNi8xkcx

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.

1.162 × 10⁹⁶(97-digit number)

11629599651707802847…48728532022194896359

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

1.162 × 10⁹⁶(97-digit number)

11629599651707802847…48728532022194896359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.162 × 10⁹⁶(97-digit number)

11629599651707802847…48728532022194896361

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

2.325 × 10⁹⁶(97-digit number)

23259199303415605694…97457064044389792719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.325 × 10⁹⁶(97-digit number)

23259199303415605694…97457064044389792721

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

4.651 × 10⁹⁶(97-digit number)

46518398606831211389…94914128088779585439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.651 × 10⁹⁶(97-digit number)

46518398606831211389…94914128088779585441

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

9.303 × 10⁹⁶(97-digit number)

93036797213662422778…89828256177559170879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.303 × 10⁹⁶(97-digit number)

93036797213662422778…89828256177559170881

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

1.860 × 10⁹⁷(98-digit number)

18607359442732484555…79656512355118341759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.860 × 10⁹⁷(98-digit number)

18607359442732484555…79656512355118341761

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 #440,859

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