Block #2,788,681

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/11/2018, 3:23:26 AM · Difficulty 11.6734 · 4,051,369 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

37bc6e8b63c42dc934e5f3779f1585bc7a52036732f3ef9717008d50ddd635d7

View on Chainz ↗

Height

#2,788,681

Difficulty

11.673377

Transactions

Size

1.09 KB

Version

Bits

0bac626b

Nonce

184,687,719

Timestamp

8/11/2018, 3:23:26 AM

Confirmations

4,051,369

Mined by

⛏️ P2SHAekAzmkPA5nq32xFLKRFjC6MeBArz8UQ7t

Merkle Root

997f7df7df39b3b9f5f4dbc46e56a38aed685172df0964400eed329008f5cb08

Transactions (5)

Coinbase6eefbdd48d3d1e…62715cae785bc3

1 in → 1 out7.3700 XPM110 B

AekAzmkP…Arz8UQ7t

7d5c1b83a0c80f…b3bc4953c82aed

2 in → 2 out14.6500 XPM306 B

Ac1euLwx…LPrXv4rR ALx143y6…dHpHRoL3

aa6a53ec376629…9df25240c19618

1 in → 2 out7.3200 XPM192 B

AMv64uDT…aEqYvY3e AexaZGZS…rgUPeZbd

3f34fa1ee9f9a0…18659ea1d507fc

1 in → 2 out7.3200 XPM192 B

AbgCCfcF…MNeV9875 AdGFnV3a…o6n2zX3x

cfe7f9a6d7501b…959246d25cbbec

1 in → 2 out3.9900 XPM226 B

AZWYn5QE…MHthHifg AMtdvM3U…ViS9pbmz

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.

1.341 × 10⁹⁵(96-digit number)

13413263294000911046…02758253887407929299

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

1.341 × 10⁹⁵(96-digit number)

13413263294000911046…02758253887407929299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.341 × 10⁹⁵(96-digit number)

13413263294000911046…02758253887407929301

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

2.682 × 10⁹⁵(96-digit number)

26826526588001822093…05516507774815858599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.682 × 10⁹⁵(96-digit number)

26826526588001822093…05516507774815858601

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

5.365 × 10⁹⁵(96-digit number)

53653053176003644187…11033015549631717199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.365 × 10⁹⁵(96-digit number)

53653053176003644187…11033015549631717201

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

1.073 × 10⁹⁶(97-digit number)

10730610635200728837…22066031099263434399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.073 × 10⁹⁶(97-digit number)

10730610635200728837…22066031099263434401

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

2.146 × 10⁹⁶(97-digit number)

21461221270401457674…44132062198526868799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.146 × 10⁹⁶(97-digit number)

21461221270401457674…44132062198526868801

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

4.292 × 10⁹⁶(97-digit number)

42922442540802915349…88264124397053737599

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 #2,788,681

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