Block #1,492,500

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2016, 12:10:36 PM · Difficulty 10.6774 · 5,324,189 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f6c5e25bd3bef948e2a8cbcee96f2556af85c52d4250aaa710fe8e76601f531

View on Chainz ↗

Height

#1,492,500

Difficulty

10.677370

Transactions

Size

6.99 KB

Version

Bits

0aad681c

Nonce

131,213,102

Timestamp

3/11/2016, 12:10:36 PM

Confirmations

5,324,189

Mined by

⛏️ P2SHAMhDrZEumhwPi85hLmEuxBaxzxUS9yuj71

Merkle Root

391fc0284b0a34651ce6d31e75f90c0d5171ec11b0184240b3b9f647b88000ef

Transactions (5)

Coinbase8658f0cd1e1160…19315dfcd6b645

1 in → 1 out8.8400 XPM110 B

AMhDrZEu…US9yuj71

8fc432ae1a3a3d…932da408917e26

1 in → 51 out96.9464 XPM1.85 KB

ASa9wJ4x…zm8gR6F1 AKX9oPq7…DeUaTZoS ALWcRwqS…KAy9F9nQ AZ2Dv6vs…YoKVyFme AToLzNHA…8kcfz3bv

e9e72cc12887ca…e341c4fdca69e7

1 in → 51 out65.4370 XPM1.85 KB

AJGxaS3r…AtxWgqbR Adsim3QN…Kvy5UmsQ AYhfsBMm…k2Zrhyvi ALgBjFS7…JjjX7HWb AddUSmgB…nsNX1H2E

71cb10d881e6ff…f379295dc1fb2a

1 in → 51 out23.8370 XPM1.85 KB

AZ3cZHxS…1qdoLqba AQyNt8HW…dNGpNRdr AV9juNpL…v9cQdRre AaSmSYsf…MwctnpJC AUAzip4H…EYhdgmXH

755a6fcd526219…a005d19724a79a

1 in → 33 out180.4096 XPM1.25 KB

AS7EhQy8…svFmz7yp AWQSckCj…C2TpkmsK AKvW4H9R…29aZZdJG AXrssTvb…hG6BTjxa ANT6FYei…mwuM7Nif

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.

2.079 × 10⁹⁴(95-digit number)

20796601103773915264…38476168702254558719

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

2.079 × 10⁹⁴(95-digit number)

20796601103773915264…38476168702254558719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.079 × 10⁹⁴(95-digit number)

20796601103773915264…38476168702254558721

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

4.159 × 10⁹⁴(95-digit number)

41593202207547830529…76952337404509117439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.159 × 10⁹⁴(95-digit number)

41593202207547830529…76952337404509117441

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

8.318 × 10⁹⁴(95-digit number)

83186404415095661058…53904674809018234879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.318 × 10⁹⁴(95-digit number)

83186404415095661058…53904674809018234881

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

1.663 × 10⁹⁵(96-digit number)

16637280883019132211…07809349618036469759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.663 × 10⁹⁵(96-digit number)

16637280883019132211…07809349618036469761

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

3.327 × 10⁹⁵(96-digit number)

33274561766038264423…15618699236072939519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.327 × 10⁹⁵(96-digit number)

33274561766038264423…15618699236072939521

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 #1,492,500

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