Block #374,086

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2014, 6:13:12 PM · Difficulty 10.4279 · 6,453,025 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2c7504a5e8c264c851c460f12ce23be9fe6834914442f3201084a82dae335b4

View on Chainz ↗

Height

#374,086

Difficulty

10.427946

Transactions

Size

866 B

Version

Bits

0a6d8ddd

Nonce

11,113

Timestamp

1/24/2014, 6:13:12 PM

Confirmations

6,453,025

Mined by

⛏️ FaRAWQBKr3YBNqdknh157YGqdQEjQsUA1Ehpd

Merkle Root

a0b167990a80379e85d0827b5c9c05844d4cb89d510de528f48e646a6ed2d43e

Transactions (4)

Coinbase6bf59fca8bbf2c…8f0fe818a06c0b

1 in → 1 out9.1800 XPM97 B

AWQBKr3Y…sUA1Ehpd

3b7b2fe28cb891…e9854acce0168e

1 in → 2 out5.0765 XPM226 B

Af66E72X…9JUxSeba Af4Dj4EH…CLw3G7Wb

8d859d5c150acf…cead31715f7df9

1 in → 2 out5.0154 XPM225 B

AeCs4oqw…q3GjK5ea AVCEgFeJ…WHLHmeek

7b6082be3b8ded…f47e5c66f10158

1 in → 2 out2.4204 XPM225 B

AXnL68UR…jsxeGUhN AG7Yt4p7…pVQXm2an

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.

3.183 × 10¹⁰¹(102-digit number)

31832362028434357694…21195345297372395199

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

3.183 × 10¹⁰¹(102-digit number)

31832362028434357694…21195345297372395199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.183 × 10¹⁰¹(102-digit number)

31832362028434357694…21195345297372395201

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

6.366 × 10¹⁰¹(102-digit number)

63664724056868715389…42390690594744790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.366 × 10¹⁰¹(102-digit number)

63664724056868715389…42390690594744790401

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

1.273 × 10¹⁰²(103-digit number)

12732944811373743077…84781381189489580799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.273 × 10¹⁰²(103-digit number)

12732944811373743077…84781381189489580801

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

2.546 × 10¹⁰²(103-digit number)

25465889622747486155…69562762378979161599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.546 × 10¹⁰²(103-digit number)

25465889622747486155…69562762378979161601

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

5.093 × 10¹⁰²(103-digit number)

50931779245494972311…39125524757958323199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.093 × 10¹⁰²(103-digit number)

50931779245494972311…39125524757958323201

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 #374,086

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