Block #411,003

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2014, 11:08:50 AM · Difficulty 10.4299 · 6,414,312 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4985ced94e59125dba5223a5e9e64ca2bc89153b85e845383281d98cf44fed3d

View on Chainz ↗

Height

#411,003

Difficulty

10.429944

Transactions

Size

425 B

Version

Bits

0a6e10cf

Nonce

222,673

Timestamp

2/19/2014, 11:08:50 AM

Confirmations

6,414,312

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c3517d12f0e6d245e392bfdcf1f9f003cd163c2b19173d6673f920fb79d50f02

Transactions (2)

Coinbaseeb6900c39c992d…09e248645ea270

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

46c0bfbc05f4e5…4594d65fd0d0bb

1 in → 2 out2.9922 XPM226 B

AXMCsXbi…aQp1hpqc AUrBZDxq…ycvbyXPS

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.

5.449 × 10⁹¹(92-digit number)

54491415264381635158…56773289105045791499

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

5.449 × 10⁹¹(92-digit number)

54491415264381635158…56773289105045791499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.449 × 10⁹¹(92-digit number)

54491415264381635158…56773289105045791501

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

1.089 × 10⁹²(93-digit number)

10898283052876327031…13546578210091582999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.089 × 10⁹²(93-digit number)

10898283052876327031…13546578210091583001

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

2.179 × 10⁹²(93-digit number)

21796566105752654063…27093156420183165999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.179 × 10⁹²(93-digit number)

21796566105752654063…27093156420183166001

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

4.359 × 10⁹²(93-digit number)

43593132211505308126…54186312840366331999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.359 × 10⁹²(93-digit number)

43593132211505308126…54186312840366332001

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

8.718 × 10⁹²(93-digit number)

87186264423010616253…08372625680732663999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.718 × 10⁹²(93-digit number)

87186264423010616253…08372625680732664001

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 #411,003

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