Block #305,878

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 5:46:24 PM · Difficulty 9.9937 · 6,488,655 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3a37a339c95affd45c097376a23dfc99e8455e88862727aa82d36e55e62d7a6

View on Chainz ↗

Height

#305,878

Difficulty

9.993735

Transactions

Size

2.20 KB

Version

Bits

09fe6566

Nonce

233,248

Timestamp

12/11/2013, 5:46:24 PM

Confirmations

6,488,655

Mined by

⛏️ aRAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

01e883ed28d33273dcac0d2e0d1c7ad76669e9222170d6bdb0cf79d8d11b12a5

Transactions (4)

Coinbase43a8d6c33dc662…1a94f0d3811ad9

1 in → 31 out9.9800 XPM1.09 KB

AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AGXewNDY…FgKQN3gK AWXYBWKP…qQAoisBJ ATnQQJPA…S8g6Z5XW

9b6cb4cac99c08…0675238b3a8167

3 in → 5 out12.6156 XPM589 B

AVCup41c…qE5u23GJ AeKNrjNj…1NEq95Ta ANd6WBPc…1qLGEEyC AcADmAoe…8iNnoMzB AcyPVp7N…dDULWcdA

5dbe94537ce7ec…946d91a6accf7b

1 in → 2 out2.9956 XPM226 B

AJQqsz7L…96fZPyPD ATrt78bB…dou8McDY

e15dd979b76c3a…618f19a6d6efca

1 in → 2 out5.4490 XPM227 B

ALF2riXH…3GiK1yLj AdyEcm7D…ymqUw7a7

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.

1.206 × 10⁹³(94-digit number)

12066205800835929544…34493135991880497919

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

1.206 × 10⁹³(94-digit number)

12066205800835929544…34493135991880497919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.206 × 10⁹³(94-digit number)

12066205800835929544…34493135991880497921

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

2.413 × 10⁹³(94-digit number)

24132411601671859089…68986271983760995839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.413 × 10⁹³(94-digit number)

24132411601671859089…68986271983760995841

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

4.826 × 10⁹³(94-digit number)

48264823203343718178…37972543967521991679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.826 × 10⁹³(94-digit number)

48264823203343718178…37972543967521991681

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

9.652 × 10⁹³(94-digit number)

96529646406687436356…75945087935043983359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.652 × 10⁹³(94-digit number)

96529646406687436356…75945087935043983361

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

1.930 × 10⁹⁴(95-digit number)

19305929281337487271…51890175870087966719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.930 × 10⁹⁴(95-digit number)

19305929281337487271…51890175870087966721

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