Block #245,923

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 6:43:35 PM · Difficulty 9.9643 · 6,562,947 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

79b4ec1dfcc6cb077fcad4208214d4d09653040a0d399c24a29a602a0fb44f85

View on Chainz ↗

Height

#245,923

Difficulty

9.964252

Transactions

Size

1.77 KB

Version

Bits

09f6d938

Nonce

53,124

Timestamp

11/5/2013, 6:43:35 PM

Confirmations

6,562,947

Mined by

⛏️ Ry<AcANo4YY1xjeppLPNm9kAdtJjYCnvnsPRDSU

Merkle Root

6a37905e0fb17d60e6917f1d0a6e7af2bba7d76e1626348fccfa16dd64f7d802

Transactions (1)

Coinbase6a37905e0fb17d…fa16dd64f7d802

1 in → 49 out10.0400 XPM1.69 KB

ANo4YY1x…vnsPRDSU ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC ARR7aRH6…ne3DXGXZ AMbCuLHZ…WSoStwkc

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.

1.991 × 10⁹³(94-digit number)

19913437690642871454…64713896631376595839

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

1.991 × 10⁹³(94-digit number)

19913437690642871454…64713896631376595839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.991 × 10⁹³(94-digit number)

19913437690642871454…64713896631376595841

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

3.982 × 10⁹³(94-digit number)

39826875381285742909…29427793262753191679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.982 × 10⁹³(94-digit number)

39826875381285742909…29427793262753191681

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

7.965 × 10⁹³(94-digit number)

79653750762571485818…58855586525506383359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.965 × 10⁹³(94-digit number)

79653750762571485818…58855586525506383361

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

1.593 × 10⁹⁴(95-digit number)

15930750152514297163…17711173051012766719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.593 × 10⁹⁴(95-digit number)

15930750152514297163…17711173051012766721

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

3.186 × 10⁹⁴(95-digit number)

31861500305028594327…35422346102025533439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.186 × 10⁹⁴(95-digit number)

31861500305028594327…35422346102025533441

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 #245,923

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