Block #471,678

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 6:05:11 PM · Difficulty 10.4354 · 6,336,197 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

61699aa7515c38aee3faf5a9da5b53aa31b849259924cd7274051907089d1180

View on Chainz ↗

Height

#471,678

Difficulty

10.435399

Transactions

Size

1.05 KB

Version

Bits

0a6f7648

Nonce

2,460,372

Timestamp

4/2/2014, 6:05:11 PM

Confirmations

6,336,197

Mined by

⛏️ P2SHAYYJe9fR2r2pYtQQjw8mwPxwmrMR2khLLF

Merkle Root

b0d568dfa84d8e71b216691994f1606e0b4c4b7493c65dde021f995c2346acae

Transactions (2)

Coinbase6e59df5dd4a817…4b68039c6a75e9

1 in → 1 out9.1800 XPM109 B

AYYJe9fR…MR2khLLF

2fc52520b8b959…09f89e042e5748

4 in → 12 out36.7800 XPM874 B

ARxECtKx…CzZwkUrj AZ6oVq47…nA7P7ADp ALHh4KEC…iRJuWFy8 AcEfJLzo…Ly8aDU8m AMeyeZ9L…gJoDemgf

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.

6.166 × 10⁹⁵(96-digit number)

61664943788897951238…57216779002990367679

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

6.166 × 10⁹⁵(96-digit number)

61664943788897951238…57216779002990367679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.166 × 10⁹⁵(96-digit number)

61664943788897951238…57216779002990367681

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

1.233 × 10⁹⁶(97-digit number)

12332988757779590247…14433558005980735359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.233 × 10⁹⁶(97-digit number)

12332988757779590247…14433558005980735361

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

2.466 × 10⁹⁶(97-digit number)

24665977515559180495…28867116011961470719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.466 × 10⁹⁶(97-digit number)

24665977515559180495…28867116011961470721

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

4.933 × 10⁹⁶(97-digit number)

49331955031118360990…57734232023922941439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.933 × 10⁹⁶(97-digit number)

49331955031118360990…57734232023922941441

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

9.866 × 10⁹⁶(97-digit number)

98663910062236721981…15468464047845882879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.866 × 10⁹⁶(97-digit number)

98663910062236721981…15468464047845882881

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

Block #471,678

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