Block #306,172

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 9:30:09 PM · Difficulty 9.9938 · 6,503,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb51d4d100f6e8aaae32b0ac3f08d07ce61ace140ee810da2e47cc912c849915

View on Chainz ↗

Height

#306,172

Difficulty

9.993830

Transactions

Size

866 B

Version

Bits

09fe6ba3

Nonce

15,606

Timestamp

12/11/2013, 9:30:09 PM

Confirmations

6,503,366

Mined by

⛏️ aRHAcM3ext6YRUPiXDZcQabLFkVZmHwtj9Qp3

Merkle Root

b11bdd921b72ceee0caa87adfff471de3adc5f40a147546ce4c28241b608d379

Transactions (1)

Coinbaseb11bdd921b72ce…c28241b608d379

1 in → 21 out10.0000 XPM777 B

AcM3ext6…Hwtj9Qp3 ARcqMJhp…RVLToQ6S AYtDvcGs…VuAcA7m7 AMRko8yH…hzixtWbJ APRdW2AC…46bvwTrN

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.

1.574 × 10⁹³(94-digit number)

15747755227305484232…23151223667424429799

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

1.574 × 10⁹³(94-digit number)

15747755227305484232…23151223667424429799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.574 × 10⁹³(94-digit number)

15747755227305484232…23151223667424429801

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

3.149 × 10⁹³(94-digit number)

31495510454610968464…46302447334848859599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.149 × 10⁹³(94-digit number)

31495510454610968464…46302447334848859601

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

6.299 × 10⁹³(94-digit number)

62991020909221936928…92604894669697719199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.299 × 10⁹³(94-digit number)

62991020909221936928…92604894669697719201

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

1.259 × 10⁹⁴(95-digit number)

12598204181844387385…85209789339395438399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.259 × 10⁹⁴(95-digit number)

12598204181844387385…85209789339395438401

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

2.519 × 10⁹⁴(95-digit number)

25196408363688774771…70419578678790876799

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 #306,172

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