Block #471,167

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 10:10:49 AM · Difficulty 10.4313 · 6,327,863 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b15c29365d3bcd12a23fe8175ef34978e9ad52db0652ad27b6ec86453f45a331

View on Chainz ↗

Height

#471,167

Difficulty

10.431269

Transactions

Size

48.45 KB

Version

Bits

0a6e67ab

Nonce

117,690,138

Timestamp

4/2/2014, 10:10:49 AM

Confirmations

6,327,863

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

062621999baf8f0ee29eae01f87b67cd00b9899f739388f420fc00cb80d389b2

Transactions (5)

Coinbasedc2d5c40a8971a…34f4bc662181ea

1 in → 1 out9.7000 XPM116 B

AbwWkWZt…kawDhufa

e3aecae894a1d7…c034a6df1b6efc

7 in → 36 out64.3200 XPM2.22 KB

AUkdqaxr…4jcbMUQ7 AKfwEQcv…uF2f3oRH AR8WV4KS…SChNuf3B AX6RyVZ9…HrhHVBnT AeXEE9bU…K7M3huKw

76a56395f855e6…32c88b2e3b2252

315 in → 2 out110.0100 XPM45.59 KB

AcFEPL6o…cGdLYbdT AaxnrQFQ…TfSy2Euj

8dfeca72872315…063911959098c9

1 in → 2 out5.0241 XPM226 B

ATqEvMER…ZEvVFT6e Aei2GMQ6…MxLiA6Dk

c15bc56fe3e9d8…c92ef5fd8b5c80

1 in → 2 out1.0806 XPM226 B

ARevM4hR…LxUGt2Uq Ac24WwPt…BSeTbxUj

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.

4.338 × 10⁹⁸(99-digit number)

43385609386670576672…08413360333975623679

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

4.338 × 10⁹⁸(99-digit number)

43385609386670576672…08413360333975623679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.338 × 10⁹⁸(99-digit number)

43385609386670576672…08413360333975623681

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

8.677 × 10⁹⁸(99-digit number)

86771218773341153344…16826720667951247359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.677 × 10⁹⁸(99-digit number)

86771218773341153344…16826720667951247361

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

1.735 × 10⁹⁹(100-digit number)

17354243754668230668…33653441335902494719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.735 × 10⁹⁹(100-digit number)

17354243754668230668…33653441335902494721

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

3.470 × 10⁹⁹(100-digit number)

34708487509336461337…67306882671804989439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.470 × 10⁹⁹(100-digit number)

34708487509336461337…67306882671804989441

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

6.941 × 10⁹⁹(100-digit number)

69416975018672922675…34613765343609978879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.941 × 10⁹⁹(100-digit number)

69416975018672922675…34613765343609978881

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