Block #251,992

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 8:12:28 AM · Difficulty 9.9706 · 6,540,218 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de35c4e6b97f29f9ca5658625826bb8f8ec68c53b32d4b1b507fec2ed7c1aaef

View on Chainz ↗

Height

#251,992

Difficulty

9.970555

Transactions

Size

1.14 KB

Version

Bits

09f8764f

Nonce

15,051

Timestamp

11/9/2013, 8:12:28 AM

Confirmations

6,540,218

Merkle Root

9097f923c863b97779d9b5ca4c348f3cfab15b868e17b5f2aba5acfaf06d9c36

Transactions (2)

Coinbase57a30322ed1574…d3e2c3d7f54ce6

1 in → 1 out10.0500 XPM109 B

ASWL9KH7…V1EMqTZ4

9bb849ad11548a…f4d05681e528d9

6 in → 2 out111.7284 XPM968 B

ASWuKUC6…pLmQgMGA AZdmkNt9…Dk8ffFeU

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.

4.578 × 10⁹⁰(91-digit number)

45781876605439119046…13899485576435759359

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

4.578 × 10⁹⁰(91-digit number)

45781876605439119046…13899485576435759359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.578 × 10⁹⁰(91-digit number)

45781876605439119046…13899485576435759361

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

9.156 × 10⁹⁰(91-digit number)

91563753210878238092…27798971152871518719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.156 × 10⁹⁰(91-digit number)

91563753210878238092…27798971152871518721

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

1.831 × 10⁹¹(92-digit number)

18312750642175647618…55597942305743037439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.831 × 10⁹¹(92-digit number)

18312750642175647618…55597942305743037441

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

3.662 × 10⁹¹(92-digit number)

36625501284351295236…11195884611486074879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.662 × 10⁹¹(92-digit number)

36625501284351295236…11195884611486074881

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

7.325 × 10⁹¹(92-digit number)

73251002568702590473…22391769222972149759

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