Block #291,879

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 10:27:41 AM · Difficulty 9.9901 · 6,514,287 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

036540b1f69827dd5db8c19df46bd3c1aaac0900b4126d3fc122e202f78cb6a8

View on Chainz ↗

Height

#291,879

Difficulty

9.990054

Transactions

Size

2.94 KB

Version

Bits

09fd742a

Nonce

396,310

Timestamp

12/3/2013, 10:27:41 AM

Confirmations

6,514,287

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

75d5d39545e592f9329c29163724fe47e82d10e5e1da805ab6cd005f533e47e7

Transactions (5)

Coinbase3aa0d06b6a06e2…da3ccdfbb5098b

1 in → 1 out10.0500 XPM110 B

AeKNrjNj…1NEq95Ta

9527dc30689cda…79eb8ca51ba07c

1 in → 2 out23973.5247 XPM225 B

AREo47Qd…bZRxM6bM AJEuzYgP…5CQFXv5x

6969f0be2bd0f6…056e7ba61c925d

3 in → 8 out23.4431 XPM658 B

AeKNrjNj…1NEq95Ta ALoDXDjp…27bFrpe5 AHG4xSSE…uGniXy6K ARq3HvGe…MJHG3U4J AQd7NAqj…KQ6cebzk

d0107254e4f0e9…a021e1f5987e24

3 in → 2 out30.2853 XPM521 B

ARC87LmU…8Tm9sTnh AcEUjB8T…7y8mLUDZ

c9bab0a8ded345…d8fbfd76305c0f

9 in → 2 out9.2977 XPM1.38 KB

ALPCFwhW…NpX1aWmB AG6Eb9hP…tjXqS4N1

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.

1.017 × 10⁹⁴(95-digit number)

10174788908295137277…81387424567683284479

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

1.017 × 10⁹⁴(95-digit number)

10174788908295137277…81387424567683284479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.017 × 10⁹⁴(95-digit number)

10174788908295137277…81387424567683284481

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

2.034 × 10⁹⁴(95-digit number)

20349577816590274554…62774849135366568959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.034 × 10⁹⁴(95-digit number)

20349577816590274554…62774849135366568961

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

4.069 × 10⁹⁴(95-digit number)

40699155633180549109…25549698270733137919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.069 × 10⁹⁴(95-digit number)

40699155633180549109…25549698270733137921

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

8.139 × 10⁹⁴(95-digit number)

81398311266361098219…51099396541466275839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.139 × 10⁹⁴(95-digit number)

81398311266361098219…51099396541466275841

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

1.627 × 10⁹⁵(96-digit number)

16279662253272219643…02198793082932551679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.627 × 10⁹⁵(96-digit number)

16279662253272219643…02198793082932551681

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