Block #318,881

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/18/2013, 4:09:53 PM · Difficulty 10.1612 · 6,476,128 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0486e36fd41663b672ff2a57a2598ffb772d08d0e12b18d1f5d7bb6cc0187a5b

View on Chainz ↗

Height

#318,881

Difficulty

10.161234

Transactions

Size

993 B

Version

Bits

0a2946a3

Nonce

9,205

Timestamp

12/18/2013, 4:09:53 PM

Confirmations

6,476,128

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

b72c36e1fdff4d95cbfbc72d6d5a2cf131ba2f3c6967e1e1a6d03722e666d357

Transactions (4)

Coinbaseb9b4d083e526a2…78b7e08c233995

1 in → 1 out9.7000 XPM110 B

AeKNrjNj…1NEq95Ta

6a194b35dbd591…756ea4ae49d3cb

2 in → 1 out62.7900 XPM338 B

AH6NJWXe…Fqzzck7J

c80a12cfd2dfa1…c7099e5a32689f

1 in → 2 out8.7492 XPM226 B

AcmJ9Bhr…MtF2X4ov AZuChMwD…kSkibHTG

289cf0c85e54b9…6210cee5b772c2

1 in → 2 out8.7492 XPM226 B

AVbg8zZ1…Tw89j3uh AQzdW4BR…Bto5KcCL

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.

4.426 × 10¹⁰²(103-digit number)

44267002730236239538…96717042508752967679

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

4.426 × 10¹⁰²(103-digit number)

44267002730236239538…96717042508752967679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.426 × 10¹⁰²(103-digit number)

44267002730236239538…96717042508752967681

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

8.853 × 10¹⁰²(103-digit number)

88534005460472479077…93434085017505935359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.853 × 10¹⁰²(103-digit number)

88534005460472479077…93434085017505935361

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

1.770 × 10¹⁰³(104-digit number)

17706801092094495815…86868170035011870719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.770 × 10¹⁰³(104-digit number)

17706801092094495815…86868170035011870721

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

3.541 × 10¹⁰³(104-digit number)

35413602184188991630…73736340070023741439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.541 × 10¹⁰³(104-digit number)

35413602184188991630…73736340070023741441

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

7.082 × 10¹⁰³(104-digit number)

70827204368377983261…47472680140047482879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.082 × 10¹⁰³(104-digit number)

70827204368377983261…47472680140047482881

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