Block #384,924

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2014, 10:57:27 AM · Difficulty 10.4024 · 6,425,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

efae24286ecb284f2a09baf11c2d159cc5fab040824491728d98834265efb7fa

View on Chainz ↗

Height

#384,924

Difficulty

10.402433

Transactions

Size

1.08 KB

Version

Bits

0a6705de

Nonce

13,940

Timestamp

2/1/2014, 10:57:27 AM

Confirmations

6,425,173

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6219ba6f19a7fb297eae8d910e178f466464272c9848e5a03c2eb3dd17fbdae2

Transactions (5)

Coinbase5afd69b4d7a9f9…a55627dff37814

1 in → 1 out9.2700 XPM110 B

AeKNrjNj…1NEq95Ta

0ac719ac371a80…8cef0ad5ad7a3b

1 in → 2 out8.1755 XPM226 B

AUkJJ18Q…4nYXgZJJ AVjJd9TW…q4HPNDVx

a3fca2d9462336…c1bccba4f73723

1 in → 2 out4.3531 XPM226 B

AHNfp7YQ…3Wi8pwVu AGVgwCRv…2r9YbV5n

88168fb49a6cc8…631458022c39c8

1 in → 2 out8.1723 XPM227 B

AJi37vdm…KMfXeaFZ AXC8ek1T…8TLim3gV

c406d997aca723…863e3ea25f2b96

1 in → 2 out6.1185 XPM227 B

AZfpuF56…n91EA9DQ AWjMy3MQ…6SDvk22A

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.

6.397 × 10⁹⁷(98-digit number)

63979009756654343955…45700398599269468159

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

6.397 × 10⁹⁷(98-digit number)

63979009756654343955…45700398599269468159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.397 × 10⁹⁷(98-digit number)

63979009756654343955…45700398599269468161

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

1.279 × 10⁹⁸(99-digit number)

12795801951330868791…91400797198538936319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.279 × 10⁹⁸(99-digit number)

12795801951330868791…91400797198538936321

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

2.559 × 10⁹⁸(99-digit number)

25591603902661737582…82801594397077872639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.559 × 10⁹⁸(99-digit number)

25591603902661737582…82801594397077872641

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

5.118 × 10⁹⁸(99-digit number)

51183207805323475164…65603188794155745279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.118 × 10⁹⁸(99-digit number)

51183207805323475164…65603188794155745281

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

1.023 × 10⁹⁹(100-digit number)

10236641561064695032…31206377588311490559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.023 × 10⁹⁹(100-digit number)

10236641561064695032…31206377588311490561

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 #384,924

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