Block #1,492,219

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2016, 7:04:57 AM · Difficulty 10.6790 · 5,350,348 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00e42824f33d58823d6e10706546e8b9080866b235d81b27cb05198bd388dc9a

View on Chainz ↗

Height

#1,492,219

Difficulty

10.679019

Transactions

Size

1.28 KB

Version

Bits

0aadd42f

Nonce

164,850,248

Timestamp

3/11/2016, 7:04:57 AM

Confirmations

5,350,348

Mined by

⛏️ P2SHARvoDmULiX3cuagN53gXRRHcM6vGzkaWSX

Merkle Root

ba372699d0e379e697ed642a0d062af7c1b037341de4771128eaf8b027a2f27f

Transactions (2)

Coinbasec0c1393d7db4b3…44b6de58297175

1 in → 1 out8.7700 XPM110 B

ARvoDmUL…vGzkaWSX

ab3b634e09dc38…460a9089c26241

1 in → 28 out184.0368 XPM1.08 KB

AMznJws3…LpVbLJfo AefvteX5…qLGU7WYr ASPLiH39…sNSndmAt AXLkjH6Q…9wXKhR9V AMKAXgk1…4BX8xfDV

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.

1.081 × 10⁹⁴(95-digit number)

10818657785805751136…79637226767500004219

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

1.081 × 10⁹⁴(95-digit number)

10818657785805751136…79637226767500004219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.081 × 10⁹⁴(95-digit number)

10818657785805751136…79637226767500004221

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

2.163 × 10⁹⁴(95-digit number)

21637315571611502272…59274453535000008439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.163 × 10⁹⁴(95-digit number)

21637315571611502272…59274453535000008441

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

4.327 × 10⁹⁴(95-digit number)

43274631143223004545…18548907070000016879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.327 × 10⁹⁴(95-digit number)

43274631143223004545…18548907070000016881

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

8.654 × 10⁹⁴(95-digit number)

86549262286446009090…37097814140000033759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.654 × 10⁹⁴(95-digit number)

86549262286446009090…37097814140000033761

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

1.730 × 10⁹⁵(96-digit number)

17309852457289201818…74195628280000067519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.730 × 10⁹⁵(96-digit number)

17309852457289201818…74195628280000067521

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 #1,492,219

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