Block #2,092,638

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/29/2017, 9:22:11 AM · Difficulty 10.8711 · 4,724,435 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ca413a47662d9f3b05420de6afd460a43e30589f329c5d76812317d73135936

View on Chainz ↗

Height

#2,092,638

Difficulty

10.871066

Transactions

Size

1.57 KB

Version

Bits

0adefe2e

Nonce

161,627,314

Timestamp

4/29/2017, 9:22:11 AM

Confirmations

4,724,435

Mined by

⛏️ P2SHAWhkHQURKRKu2RF5EvR4KJeVQF1V3PY9Yw

Merkle Root

85acd0f45b1afe1c574fe3dd04811b3f056833a8c0e7ae65193665b88b010b74

Transactions (2)

Coinbase9afe506d0232de…dd4b0f470f24fc

1 in → 1 out8.4800 XPM109 B

AWhkHQUR…1V3PY9Yw

59bb7980b6d661…ba1d56b493b83e

9 in → 2 out530.2829 XPM1.38 KB

AMYNEfMP…qtivh1zM AaENA1Yg…1VfiCW5X

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.

1.136 × 10⁹⁷(98-digit number)

11360969700484743962…10871828926054399999

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

1.136 × 10⁹⁷(98-digit number)

11360969700484743962…10871828926054399999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.136 × 10⁹⁷(98-digit number)

11360969700484743962…10871828926054400001

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

2.272 × 10⁹⁷(98-digit number)

22721939400969487925…21743657852108799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.272 × 10⁹⁷(98-digit number)

22721939400969487925…21743657852108800001

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

4.544 × 10⁹⁷(98-digit number)

45443878801938975851…43487315704217599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.544 × 10⁹⁷(98-digit number)

45443878801938975851…43487315704217600001

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

9.088 × 10⁹⁷(98-digit number)

90887757603877951702…86974631408435199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.088 × 10⁹⁷(98-digit number)

90887757603877951702…86974631408435200001

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

1.817 × 10⁹⁸(99-digit number)

18177551520775590340…73949262816870399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.817 × 10⁹⁸(99-digit number)

18177551520775590340…73949262816870400001

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

3.635 × 10⁹⁸(99-digit number)

36355103041551180680…47898525633740799999

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 #2,092,638

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