Block #379,088

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 7:40:43 AM · Difficulty 10.4144 · 6,429,343 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ab944634e741083aba9c57e37766b518fd290da51e19621bcd55cf4a018279c6

View on Chainz ↗

Height

#379,088

Difficulty

10.414386

Transactions

Size

651 B

Version

Bits

0a6a1537

Nonce

133,703

Timestamp

1/28/2014, 7:40:43 AM

Confirmations

6,429,343

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

0ee77cf11eb08ee69526f3ce96bc7741203d351f42ec8c2ba0ae9bfdecd8bc33

Transactions (3)

Coinbaseece1acbf32418d…8cd608ece3116a

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

d6031858e972d7…09c38ca50a1341

1 in → 2 out1.0101 XPM225 B

ASziQ5sY…9mSExUG6 AXWL6kKm…Ant1hKrh

d700d42bac1cc5…f8b75d0b74bee7

1 in → 2 out6.0388 XPM225 B

AaFRhwKA…1KdZyY7M AFreewNR…WwhUuhEf

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.

6.494 × 10⁹⁶(97-digit number)

64941266582171748831…39412556076977367999

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

6.494 × 10⁹⁶(97-digit number)

64941266582171748831…39412556076977367999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.494 × 10⁹⁶(97-digit number)

64941266582171748831…39412556076977368001

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

1.298 × 10⁹⁷(98-digit number)

12988253316434349766…78825112153954735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.298 × 10⁹⁷(98-digit number)

12988253316434349766…78825112153954736001

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

2.597 × 10⁹⁷(98-digit number)

25976506632868699532…57650224307909471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.597 × 10⁹⁷(98-digit number)

25976506632868699532…57650224307909472001

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

5.195 × 10⁹⁷(98-digit number)

51953013265737399065…15300448615818943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.195 × 10⁹⁷(98-digit number)

51953013265737399065…15300448615818944001

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

1.039 × 10⁹⁸(99-digit number)

10390602653147479813…30600897231637887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.039 × 10⁹⁸(99-digit number)

10390602653147479813…30600897231637888001

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 #379,088

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