Block #254,481

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 5:59:51 PM · Difficulty 9.9732 · 6,550,869 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

49c5bc633ef3e29951f4ca51f0777c226348c8968074de0695e97ebf8dd2b972

View on Chainz ↗

Height

#254,481

Difficulty

9.973198

Transactions

Size

2.23 KB

Version

Bits

09f9237b

Nonce

8,718

Timestamp

11/10/2013, 5:59:51 PM

Confirmations

6,550,869

Mined by

⛏️ aRASnU18rtm4iXEFBwCeEA6xYy9FoVkGMAam

Merkle Root

f40a5475b1ff544c946781fecfeb05a726261227c10193ad5b5ddb25070a12ab

Transactions (2)

Coinbase37ff3a5344789f…d1561d4eb2253b

1 in → 56 out10.0200 XPM1.92 KB

ASnU18rt…oVkGMAam AKXeSXzu…yeuNjvhB AQtzUSwq…htAuF3yC AQ5RhuRd…YsXbXRaz AKDTDDtx…iqvw9cdY

d9a07fb68b9b23…8de4770b375a59

1 in → 2 out5.9963 XPM226 B

AQbUdHtf…NpfPCzBP Aek6qbEU…njKqffFB

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.

7.086 × 10⁹⁷(98-digit number)

70864358418782152274…96750900595409879039

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

7.086 × 10⁹⁷(98-digit number)

70864358418782152274…96750900595409879039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.086 × 10⁹⁷(98-digit number)

70864358418782152274…96750900595409879041

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

1.417 × 10⁹⁸(99-digit number)

14172871683756430454…93501801190819758079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.417 × 10⁹⁸(99-digit number)

14172871683756430454…93501801190819758081

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

2.834 × 10⁹⁸(99-digit number)

28345743367512860909…87003602381639516159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.834 × 10⁹⁸(99-digit number)

28345743367512860909…87003602381639516161

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

5.669 × 10⁹⁸(99-digit number)

56691486735025721819…74007204763279032319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.669 × 10⁹⁸(99-digit number)

56691486735025721819…74007204763279032321

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

1.133 × 10⁹⁹(100-digit number)

11338297347005144363…48014409526558064639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.133 × 10⁹⁹(100-digit number)

11338297347005144363…48014409526558064641

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