Block #404,118

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2014, 3:11:29 PM · Difficulty 10.4344 · 6,399,195 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c253b0596ae5bd4cf09c921967b0cd18b76eddd17c1e2de4dc6089a747a8755c

View on Chainz ↗

Height

#404,118

Difficulty

10.434447

Transactions

Size

899 B

Version

Bits

0a6f37eb

Nonce

286,348

Timestamp

2/14/2014, 3:11:29 PM

Confirmations

6,399,195

Mined by

⛏️ *lAMW1p9oTkBzM1hi3okaKfJzfWi2TzdaZxH

Merkle Root

4bdc3745799949faf797f1a5458cac3f76ef4764ad2515739bd5e95176a53e5e

Transactions (1)

Coinbase4bdc3745799949…d5e95176a53e5e

1 in → 22 out9.1700 XPM811 B

AMW1p9oT…2TzdaZxH AcgDwGo8…BBFwbjVo AZr7Ptuw…CM4Yw5jq AMN4weDS…7ToVBkgW AdxgJDvy…HK8Y4Dsr

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.

5.921 × 10⁸⁸(89-digit number)

59213815948879865094…55626410741040470599

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

5.921 × 10⁸⁸(89-digit number)

59213815948879865094…55626410741040470599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.921 × 10⁸⁸(89-digit number)

59213815948879865094…55626410741040470601

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

1.184 × 10⁸⁹(90-digit number)

11842763189775973018…11252821482080941199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.184 × 10⁸⁹(90-digit number)

11842763189775973018…11252821482080941201

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

2.368 × 10⁸⁹(90-digit number)

23685526379551946037…22505642964161882399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.368 × 10⁸⁹(90-digit number)

23685526379551946037…22505642964161882401

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

4.737 × 10⁸⁹(90-digit number)

47371052759103892075…45011285928323764799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.737 × 10⁸⁹(90-digit number)

47371052759103892075…45011285928323764801

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

9.474 × 10⁸⁹(90-digit number)

94742105518207784151…90022571856647529599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.474 × 10⁸⁹(90-digit number)

94742105518207784151…90022571856647529601

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