Block #311,384

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/14/2013, 1:19:00 PM · Difficulty 9.9955 · 6,498,074 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43d021356ec150791e9fd9fcea4f5ad4ffcbf8dbce3c9103d7bb5afca3529953

View on Chainz ↗

Height

#311,384

Difficulty

9.995453

Transactions

Size

1.08 KB

Version

Bits

09fed608

Nonce

25,092

Timestamp

12/14/2013, 1:19:00 PM

Confirmations

6,498,074

Mined by

⛏️ P2SHAPpAmzuiarcDRTEE9yddUu8j7EbKYJJ5pB

Merkle Root

e417049f9779d53b0173964be191afe763d13d7a6673917c26938d2a7e3dad4a

Transactions (5)

Coinbase6afbbb41b90835…46af5f8ed1c092

1 in → 1 out10.0300 XPM109 B

APpAmzui…bKYJJ5pB

462eeb22e69d3f…e4d2b02b0d5a7d

1 in → 2 out5.8676 XPM226 B

Ae1VPxBf…4hG7rzG4 AZsM7LBg…QGyFU2dU

c8517a4d9d3650…63519682cc77ed

1 in → 2 out4.8258 XPM225 B

AZwyMUeE…rxMQeLU7 ANyBiXTp…zyi7aRdT

53087b7034df58…e755854ad94964

1 in → 2 out2.7087 XPM226 B

AeXusgNw…ekjWgzff AHykpSZT…BupuqJ34

55a4aca624d5bb…7d625c7e46d4f6

1 in → 2 out5.8485 XPM227 B

AYGiZnb5…uAPNfLQr AVfGY1He…FvgUxb9c

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.

5.924 × 10⁹¹(92-digit number)

59244683317173424529…49726943346753567589

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

5.924 × 10⁹¹(92-digit number)

59244683317173424529…49726943346753567589

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.924 × 10⁹¹(92-digit number)

59244683317173424529…49726943346753567591

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

1.184 × 10⁹²(93-digit number)

11848936663434684905…99453886693507135179

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.184 × 10⁹²(93-digit number)

11848936663434684905…99453886693507135181

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

2.369 × 10⁹²(93-digit number)

23697873326869369811…98907773387014270359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.369 × 10⁹²(93-digit number)

23697873326869369811…98907773387014270361

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

4.739 × 10⁹²(93-digit number)

47395746653738739623…97815546774028540719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.739 × 10⁹²(93-digit number)

47395746653738739623…97815546774028540721

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

9.479 × 10⁹²(93-digit number)

94791493307477479246…95631093548057081439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #311,384

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