Block #378,204

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 3:48:58 PM · Difficulty 10.4221 · 6,432,614 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

843a5502e6f5f5b0159f0d53ca63832b056190c6dc5840b1f7e0963dd542403e

View on Chainz ↗

Height

#378,204

Difficulty

10.422124

Transactions

Size

1.73 KB

Version

Bits

0a6c104b

Nonce

78,255

Timestamp

1/27/2014, 3:48:58 PM

Confirmations

6,432,614

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ad90c8410c9c65b7f2350353262ed4ef62fb9ed8e2fd821dbb6507acf78b2d3d

Transactions (4)

Coinbaseae88c76be63c38…d7c5ec40883605

1 in → 1 out9.2200 XPM110 B

AeKNrjNj…1NEq95Ta

fa80861f8820ea…deb10301910bc0

6 in → 2 out5.0376 XPM964 B

APJehNtw…V5zRsxsi AGEn2Fbj…sWUeo5bn

e639b3f305d302…dca6e3add1079f

2 in → 2 out4.3303 XPM376 B

AXxVGZA1…drQtBbDz AdiVTH4e…gT2mH8U3

d429e5915858d4…dbcab326e94ed8

1 in → 2 out1.6502 XPM226 B

AaTa1TJW…CS1ZqFKG ALrSHZZv…hwPyY6qW

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.

4.717 × 10⁹⁶(97-digit number)

47179821670104302578…81748368037228634239

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

4.717 × 10⁹⁶(97-digit number)

47179821670104302578…81748368037228634239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.717 × 10⁹⁶(97-digit number)

47179821670104302578…81748368037228634241

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

9.435 × 10⁹⁶(97-digit number)

94359643340208605157…63496736074457268479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.435 × 10⁹⁶(97-digit number)

94359643340208605157…63496736074457268481

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

1.887 × 10⁹⁷(98-digit number)

18871928668041721031…26993472148914536959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.887 × 10⁹⁷(98-digit number)

18871928668041721031…26993472148914536961

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

3.774 × 10⁹⁷(98-digit number)

37743857336083442062…53986944297829073919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.774 × 10⁹⁷(98-digit number)

37743857336083442062…53986944297829073921

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

7.548 × 10⁹⁷(98-digit number)

75487714672166884125…07973888595658147839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.548 × 10⁹⁷(98-digit number)

75487714672166884125…07973888595658147841

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 #378,204

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