Block #299,863

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 6:04:13 AM · Difficulty 9.9922 · 6,504,052 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2edd8f88455183df493ea07fdf1fd48ba053a2d548b0e831299ee1b22433d547

View on Chainz ↗

Height

#299,863

Difficulty

9.992164

Transactions

Size

1.18 KB

Version

Bits

09fdfe7d

Nonce

1,925

Timestamp

12/8/2013, 6:04:13 AM

Confirmations

6,504,052

Mined by

⛏️ WaR\#Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

7f1ee001c11e1e367da9a81337c58e29be2368dce61972b2e786b6549bc56e62

Transactions (1)

Coinbase7f1ee001c11e1e…86b6549bc56e62

1 in → 31 out9.9800 XPM1.09 KB

Ad9pSzHt…cpJ3y2zz ASWX42VM…XypQABkY ARYnzc2o…oDhhtZPZ AU3a838C…R83Vuk6M Ae58nAEb…GFUA15fv

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.

1.149 × 10⁹⁵(96-digit number)

11496579353820582184…62251475250668877489

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

1.149 × 10⁹⁵(96-digit number)

11496579353820582184…62251475250668877489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.149 × 10⁹⁵(96-digit number)

11496579353820582184…62251475250668877491

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

2.299 × 10⁹⁵(96-digit number)

22993158707641164368…24502950501337754979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.299 × 10⁹⁵(96-digit number)

22993158707641164368…24502950501337754981

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

4.598 × 10⁹⁵(96-digit number)

45986317415282328736…49005901002675509959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.598 × 10⁹⁵(96-digit number)

45986317415282328736…49005901002675509961

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

9.197 × 10⁹⁵(96-digit number)

91972634830564657473…98011802005351019919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.197 × 10⁹⁵(96-digit number)

91972634830564657473…98011802005351019921

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

1.839 × 10⁹⁶(97-digit number)

18394526966112931494…96023604010702039839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.839 × 10⁹⁶(97-digit number)

18394526966112931494…96023604010702039841

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