Block #2,678,316

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/26/2018, 5:31:15 AM · Difficulty 11.6941 · 4,163,988 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c748b6d162aa49674a93d558fd7e6ce6f892702f4dc5dbfe5cd416c9f94527f

View on Chainz ↗

Height

#2,678,316

Difficulty

11.694059

Transactions

Size

689 B

Version

Bits

0bb1ade2

Nonce

1,662,983,443

Timestamp

5/26/2018, 5:31:15 AM

Confirmations

4,163,988

Mined by

⛏️ P2SHASDuJSWbwYtfAtHLSZR52regizFiM4PdXz

Merkle Root

79317f0b9b7b5404e92cbc0fa11b39b233b6f08cf82883c0e2acaffa0ea848a4

Transactions (2)

Coinbase9dff0e7f4625cb…07e54cffa671ea

1 in → 1 out7.3100 XPM110 B

ASDuJSWb…FiM4PdXz

2dc2b370518b92…25688faeba4ead

3 in → 2 out11.2600 XPM488 B

APVKWthF…PMMxwRoz AJFrfsDU…S9dd5N7c

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.

5.554 × 10⁹⁶(97-digit number)

55541022282952470835…66735924414404567039

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

5.554 × 10⁹⁶(97-digit number)

55541022282952470835…66735924414404567039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.554 × 10⁹⁶(97-digit number)

55541022282952470835…66735924414404567041

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

1.110 × 10⁹⁷(98-digit number)

11108204456590494167…33471848828809134079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.110 × 10⁹⁷(98-digit number)

11108204456590494167…33471848828809134081

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

2.221 × 10⁹⁷(98-digit number)

22216408913180988334…66943697657618268159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.221 × 10⁹⁷(98-digit number)

22216408913180988334…66943697657618268161

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

4.443 × 10⁹⁷(98-digit number)

44432817826361976668…33887395315236536319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.443 × 10⁹⁷(98-digit number)

44432817826361976668…33887395315236536321

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

8.886 × 10⁹⁷(98-digit number)

88865635652723953336…67774790630473072639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.886 × 10⁹⁷(98-digit number)

88865635652723953336…67774790630473072641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.777 × 10⁹⁸(99-digit number)

17773127130544790667…35549581260946145279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,678,316

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