Block #643,091

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/22/2014, 4:21:38 AM · Difficulty 10.9569 · 6,151,959 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5c341ad57c92b442b585a396086d775af2e746c8c2bdf471f39dc4c00a37245

View on Chainz ↗

Height

#643,091

Difficulty

10.956885

Transactions

Size

660 B

Version

Bits

0af4f66d

Nonce

899,551,510

Timestamp

7/22/2014, 4:21:38 AM

Confirmations

6,151,959

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c134efd67dd3e917d77524381ec18e567a6f6617fc27015a9ab536a4d19472e9

Transactions (3)

Coinbase2747b562258eb0…2cd2dbdfcbff2b

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

4051fadbc8f038…b36de83cd28125

1 in → 2 out4.3331 XPM227 B

AWhWNAtg…UpNHuVaR ALz3uSwR…DHKjj4EL

256ec9407385d2…320a9705cb4fe4

1 in → 2 out3.2851 XPM225 B

ASoFCbWu…nPRsD59Y AL2DJ8hG…aDfUdn15

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.

1.263 × 10⁹⁹(100-digit number)

12632566928694970553…13145471630231974399

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

1.263 × 10⁹⁹(100-digit number)

12632566928694970553…13145471630231974399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.263 × 10⁹⁹(100-digit number)

12632566928694970553…13145471630231974401

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

2.526 × 10⁹⁹(100-digit number)

25265133857389941107…26290943260463948799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.526 × 10⁹⁹(100-digit number)

25265133857389941107…26290943260463948801

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

5.053 × 10⁹⁹(100-digit number)

50530267714779882214…52581886520927897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.053 × 10⁹⁹(100-digit number)

50530267714779882214…52581886520927897601

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

1.010 × 10¹⁰⁰(101-digit number)

10106053542955976442…05163773041855795199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.010 × 10¹⁰⁰(101-digit number)

10106053542955976442…05163773041855795201

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

2.021 × 10¹⁰⁰(101-digit number)

20212107085911952885…10327546083711590399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.021 × 10¹⁰⁰(101-digit number)

20212107085911952885…10327546083711590401

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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