Block #468,677

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 4:16:00 PM · Difficulty 10.4329 · 6,327,272 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

122e90b009d0d83e06b0d7ae27e5b7e0693831eca37b479817f7f9993aa90d2a

View on Chainz ↗

Height

#468,677

Difficulty

10.432927

Transactions

Size

2.09 KB

Version

Bits

0a6ed44b

Nonce

45,087

Timestamp

3/31/2014, 4:16:00 PM

Confirmations

6,327,272

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

bb413c2be03b348351f200cbdcf70de4192f892c668dcd65bd5d28c1e90a9776

Transactions (5)

Coinbase94d64d60805c00…0faae71c8fe9bb

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

10e7cc33b2710e…411fae4aaf8a46

6 in → 2 out18.4207 XPM965 B

AJmtPNba…F7KiMfUa ANBKo68j…FknjdrB2

1f6e0641f8364e…dafc9d2293ef90

1 in → 2 out5.5207 XPM227 B

AYY1mork…ZYJ2AjiN AGCmTSw4…QNSsCSPC

16e4f9d5a5d14b…be82f5ce8dd27e

2 in → 2 out1.0402 XPM373 B

ANZrCvBT…xiXxUYGw AQpg5vJa…zMdKpHtn

a1a78d4899092d…de21842dedb32d

2 in → 2 out5.7298 XPM374 B

AYybT5gf…KAFYxdVH AaVnd82B…X2x3WMeC

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.

6.326 × 10⁹²(93-digit number)

63268644885028511376…30495757849215733759

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

6.326 × 10⁹²(93-digit number)

63268644885028511376…30495757849215733759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.326 × 10⁹²(93-digit number)

63268644885028511376…30495757849215733761

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

1.265 × 10⁹³(94-digit number)

12653728977005702275…60991515698431467519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.265 × 10⁹³(94-digit number)

12653728977005702275…60991515698431467521

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

2.530 × 10⁹³(94-digit number)

25307457954011404550…21983031396862935039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.530 × 10⁹³(94-digit number)

25307457954011404550…21983031396862935041

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

5.061 × 10⁹³(94-digit number)

50614915908022809101…43966062793725870079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.061 × 10⁹³(94-digit number)

50614915908022809101…43966062793725870081

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

1.012 × 10⁹⁴(95-digit number)

10122983181604561820…87932125587451740159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.012 × 10⁹⁴(95-digit number)

10122983181604561820…87932125587451740161

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