Block #2,184,373

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/29/2017, 8:19:21 AM · Difficulty 10.9429 · 4,658,211 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

05c8788ea2cb989cb15f6c2dcf144d755200ccc2f211cf0227c6b4b56f637e17

View on Chainz ↗

Height

#2,184,373

Difficulty

10.942903

Transactions

Size

427 B

Version

Bits

0af1621c

Nonce

12,239,394

Timestamp

6/29/2017, 8:19:21 AM

Confirmations

4,658,211

Mined by

⛏️ P2SHAahasHP9GcZEDF3qEzWHF8FW1kBAvCJkZ7

Merkle Root

9c75b48a0f9d0c7caa30ed20113e621545c30b71b93ab54f549b08e06ea9c230

Transactions (2)

Coinbase70e44a18ee6868…8af8fb0776a7aa

1 in → 1 out8.3500 XPM110 B

AahasHP9…BAvCJkZ7

46b9908f7d9b48…0913ac3651392e

1 in → 2 out495.0800 XPM227 B

ASSvekTA…b9nJpVv7 AammHJuN…yaRcHuV7

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.

1.510 × 10⁹⁴(95-digit number)

15102743044872631245…24587541572586389219

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

1.510 × 10⁹⁴(95-digit number)

15102743044872631245…24587541572586389219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.510 × 10⁹⁴(95-digit number)

15102743044872631245…24587541572586389221

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

3.020 × 10⁹⁴(95-digit number)

30205486089745262491…49175083145172778439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.020 × 10⁹⁴(95-digit number)

30205486089745262491…49175083145172778441

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

6.041 × 10⁹⁴(95-digit number)

60410972179490524983…98350166290345556879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.041 × 10⁹⁴(95-digit number)

60410972179490524983…98350166290345556881

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

1.208 × 10⁹⁵(96-digit number)

12082194435898104996…96700332580691113759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.208 × 10⁹⁵(96-digit number)

12082194435898104996…96700332580691113761

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

2.416 × 10⁹⁵(96-digit number)

24164388871796209993…93400665161382227519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.416 × 10⁹⁵(96-digit number)

24164388871796209993…93400665161382227521

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

4.832 × 10⁹⁵(96-digit number)

48328777743592419987…86801330322764455039

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 #2,184,373

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