Block #822,047

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/22/2014, 12:30:41 AM · Difficulty 10.9763 · 6,004,575 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b1bb682e1019cee826e3d52161cb098397369eb5c820d05546eda1df4ee699f6

View on Chainz ↗

Height

#822,047

Difficulty

10.976256

Transactions

Size

885 B

Version

Bits

0af9ebf2

Nonce

851,482,752

Timestamp

11/22/2014, 12:30:41 AM

Confirmations

6,004,575

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5c409246438c91e439e3bb26905fceb74c62ebc0117b049b1e975af3db522388

Transactions (4)

Coinbase9d0875f173a5b4…6d49d5f21ad9a2

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

bd6985638e72b3…8b2f2b4d75b77c

1 in → 2 out5.3111 XPM226 B

AQY2eotr…tHUNnQoW AYRYBTrk…4pp2BjKS

8bca447ee071c1…13ef04af2921a3

1 in → 2 out4.6470 XPM226 B

AcKGvUdY…tUzNGhJ1 AHCiDP27…ARKmcQk2

26f9ccd93afc42…ea82853469d5a8

1 in → 2 out2.1974 XPM226 B

AHzrifkP…KunrEPhv AXrTw46X…e1dGvSFf

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.

2.174 × 10⁹⁶(97-digit number)

21748542214384068745…83896983197109837839

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

2.174 × 10⁹⁶(97-digit number)

21748542214384068745…83896983197109837839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.174 × 10⁹⁶(97-digit number)

21748542214384068745…83896983197109837841

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

4.349 × 10⁹⁶(97-digit number)

43497084428768137490…67793966394219675679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.349 × 10⁹⁶(97-digit number)

43497084428768137490…67793966394219675681

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

8.699 × 10⁹⁶(97-digit number)

86994168857536274981…35587932788439351359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.699 × 10⁹⁶(97-digit number)

86994168857536274981…35587932788439351361

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

1.739 × 10⁹⁷(98-digit number)

17398833771507254996…71175865576878702719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.739 × 10⁹⁷(98-digit number)

17398833771507254996…71175865576878702721

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

3.479 × 10⁹⁷(98-digit number)

34797667543014509992…42351731153757405439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.479 × 10⁹⁷(98-digit number)

34797667543014509992…42351731153757405441

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

6.959 × 10⁹⁷(98-digit number)

69595335086029019984…84703462307514810879

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 #822,047

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