Block #2,178,628

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/26/2017, 5:35:46 AM · Difficulty 10.9265 · 4,638,069 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c11e21a7218aa456791b01884235dacfdc9640f24cf95e61d32ad6e26b4906f

View on Chainz ↗

Height

#2,178,628

Difficulty

10.926475

Transactions

Size

721 B

Version

Bits

0aed2d7b

Nonce

1,663,593,361

Timestamp

6/26/2017, 5:35:46 AM

Confirmations

4,638,069

Mined by

⛏️ P2SHAah1aisnT6MnMa3UzHRXJNFdSABCMYTisH

Merkle Root

7738c7ff333b1550e8e4680ba6b595fc32e93add8857c7c49cf717173579e231

Transactions (2)

Coinbase747b86aaa2a32d…43d19d2abbc67e

1 in → 1 out8.3700 XPM110 B

Aah1aisn…BCMYTisH

5c927a2355d467…8b2da4ce5c86e1

3 in → 2 out346.1825 XPM521 B

AL2yEmuL…gF5tSxVL AVB8Kqgj…zUanL8Tf

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.

1.507 × 10⁹⁴(95-digit number)

15076530642210137993…99372265099109841839

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

1.507 × 10⁹⁴(95-digit number)

15076530642210137993…99372265099109841839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.507 × 10⁹⁴(95-digit number)

15076530642210137993…99372265099109841841

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

3.015 × 10⁹⁴(95-digit number)

30153061284420275986…98744530198219683679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.015 × 10⁹⁴(95-digit number)

30153061284420275986…98744530198219683681

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

6.030 × 10⁹⁴(95-digit number)

60306122568840551973…97489060396439367359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.030 × 10⁹⁴(95-digit number)

60306122568840551973…97489060396439367361

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

1.206 × 10⁹⁵(96-digit number)

12061224513768110394…94978120792878734719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.206 × 10⁹⁵(96-digit number)

12061224513768110394…94978120792878734721

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

2.412 × 10⁹⁵(96-digit number)

24122449027536220789…89956241585757469439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.412 × 10⁹⁵(96-digit number)

24122449027536220789…89956241585757469441

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 #2,178,628

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