Block #375,273

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 2:50:02 PM · Difficulty 10.4224 · 6,430,811 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8dbbc2030710d0db93a885233419b3235556d47b416b1f3d2e1523d6f18eed1c

View on Chainz ↗

Height

#375,273

Difficulty

10.422377

Transactions

Size

1.08 KB

Version

Bits

0a6c20e8

Nonce

30,190

Timestamp

1/25/2014, 2:50:02 PM

Confirmations

6,430,811

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

726701728d0a1e3fee368e769949a2793889d9d5d0556aaba57e52ef46a3f199

Transactions (5)

Coinbase44cd3f6fa2b965…f334b39f37a2c6

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

208f057de9782e…1a1afc8a7d19da

1 in → 2 out9.1600 XPM225 B

Ae6HvJUV…oQdUWM2y Ac8LYUfs…Z6r9iyJ4

50655c58659058…75359bb3733283

1 in → 2 out9.1600 XPM226 B

AKRxnPyu…9B9Hy3g4 AGqzyXkc…7GgfdMi9

6fa4290f9e8362…ac267facd5246e

1 in → 2 out9.1600 XPM225 B

AKD8qAKh…PyxhtHU6 AGjXRvvn…dL3EHMT1

1945a5e8357f43…4b6c3554ae0aa8

1 in → 2 out8.1492 XPM225 B

AKT45Xu6…SEh9w2mm AVF3iUrb…MvgDtGv7

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.

1.462 × 10¹⁰⁰(101-digit number)

14626457711693818468…58026713813567805439

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

1.462 × 10¹⁰⁰(101-digit number)

14626457711693818468…58026713813567805439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.462 × 10¹⁰⁰(101-digit number)

14626457711693818468…58026713813567805441

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

2.925 × 10¹⁰⁰(101-digit number)

29252915423387636937…16053427627135610879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.925 × 10¹⁰⁰(101-digit number)

29252915423387636937…16053427627135610881

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

5.850 × 10¹⁰⁰(101-digit number)

58505830846775273874…32106855254271221759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.850 × 10¹⁰⁰(101-digit number)

58505830846775273874…32106855254271221761

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

1.170 × 10¹⁰¹(102-digit number)

11701166169355054774…64213710508542443519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.170 × 10¹⁰¹(102-digit number)

11701166169355054774…64213710508542443521

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

2.340 × 10¹⁰¹(102-digit number)

23402332338710109549…28427421017084887039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.340 × 10¹⁰¹(102-digit number)

23402332338710109549…28427421017084887041

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