Block #302,288

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/9/2013, 5:37:45 PM · Difficulty 9.9927 · 6,493,435 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

969696fb191e2a51e4f4beef337276788bf584bfda51959603bb5a5671b6d435

View on Chainz ↗

Height

#302,288

Difficulty

9.992678

Transactions

Size

3.02 KB

Version

Bits

09fe2024

Nonce

79,273

Timestamp

12/9/2013, 5:37:45 PM

Confirmations

6,493,435

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9489a3edd2d07b3c88167261c90632a1369487f06737fad3653d595e29b4c851

Transactions (4)

Coinbasef69b8aa2e3e47a…d07768a631c0be

1 in → 1 out10.0500 XPM110 B

AeKNrjNj…1NEq95Ta

a994ae181a1d5f…f2edd2a57ed168

2 in → 3 out32.7632 XPM407 B

AQWqYit2…FZ1A1KZb AQcfmCpQ…5NThrUnA AbpQYve5…ar9isbkM

76cd687241913e…7009638e9d7b20

1 in → 2 out2.1001 XPM225 B

AZdT4ky3…kkR5Ga71 AQyYuP6H…MvSLoLyP

413ecacbbf2e63…5db9c1ab7058e4

15 in → 1 out6.1999 XPM2.21 KB

ALAFH3kk…VBdunEdz

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.

2.192 × 10⁹³(94-digit number)

21927074725439504304…59731510929981998039

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

2.192 × 10⁹³(94-digit number)

21927074725439504304…59731510929981998039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.192 × 10⁹³(94-digit number)

21927074725439504304…59731510929981998041

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

4.385 × 10⁹³(94-digit number)

43854149450879008609…19463021859963996079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.385 × 10⁹³(94-digit number)

43854149450879008609…19463021859963996081

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

8.770 × 10⁹³(94-digit number)

87708298901758017218…38926043719927992159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.770 × 10⁹³(94-digit number)

87708298901758017218…38926043719927992161

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

1.754 × 10⁹⁴(95-digit number)

17541659780351603443…77852087439855984319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.754 × 10⁹⁴(95-digit number)

17541659780351603443…77852087439855984321

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

3.508 × 10⁹⁴(95-digit number)

35083319560703206887…55704174879711968639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.508 × 10⁹⁴(95-digit number)

35083319560703206887…55704174879711968641

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