Block #398,926

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 2:36:55 AM · Difficulty 10.4193 · 6,409,064 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b7dd14317ef6eab8316def4b91396a19954a4df33526da362be261490968e70e

View on Chainz ↗

Height

#398,926

Difficulty

10.419253

Transactions

Size

2.07 KB

Version

Bits

0a6b542d

Nonce

7,382

Timestamp

2/11/2014, 2:36:55 AM

Confirmations

6,409,064

Mined by

⛏️ NY9}Acs9SHrkBk52E7r7T3v7yemDoFQJSB8SFG

Merkle Root

619c84a23a1ef4cc30b54175147698ed5192b7937ee1d4ac6fdfc941bd5a6d59

Transactions (3)

Coinbasefad4e113b4b385…9650befa7f9704

1 in → 24 out9.2200 XPM879 B

Acs9SHrk…QJSB8SFG AZuKpVkB…HFoeLG6t AZqjMFvv…G8aw2zC8 AczyTBWn…bEQQj33u ATp4jJhs…TbSgR8Qb

902fc3e55c8bcb…aec9815e6b73ac

3 in → 2 out875.0100 XPM522 B

AW2qyQMY…3UVTNgpm ANAsPPYb…ncGEHyJa

fa095e3c626307…4eb1f472b24abf

3 in → 7 out19.0271 XPM624 B

AeewPG9w…zGhNLPe4 Aeff3baB…A5fkk3mo AMurAYrb…3iomaSF2 Aao9p1b1…7FLAEmZp AWjvkJwz…JbcQNttY

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.

7.612 × 10⁹⁸(99-digit number)

76124909301129463396…74343739587813095359

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

7.612 × 10⁹⁸(99-digit number)

76124909301129463396…74343739587813095359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.612 × 10⁹⁸(99-digit number)

76124909301129463396…74343739587813095361

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

1.522 × 10⁹⁹(100-digit number)

15224981860225892679…48687479175626190719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.522 × 10⁹⁹(100-digit number)

15224981860225892679…48687479175626190721

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

3.044 × 10⁹⁹(100-digit number)

30449963720451785358…97374958351252381439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.044 × 10⁹⁹(100-digit number)

30449963720451785358…97374958351252381441

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

6.089 × 10⁹⁹(100-digit number)

60899927440903570717…94749916702504762879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.089 × 10⁹⁹(100-digit number)

60899927440903570717…94749916702504762881

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

1.217 × 10¹⁰⁰(101-digit number)

12179985488180714143…89499833405009525759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.217 × 10¹⁰⁰(101-digit number)

12179985488180714143…89499833405009525761

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 #398,926

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