Block #317,742

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/17/2013, 9:49:56 PM · Difficulty 10.1540 · 6,489,607 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58301e9e2076cd0f85afca3e28a1c2af014bef5e704050f5c7ac5c7ea28ce296

View on Chainz ↗

Height

#317,742

Difficulty

10.154008

Transactions

Size

1.89 KB

Version

Bits

0a276d12

Nonce

11,520

Timestamp

12/17/2013, 9:49:56 PM

Confirmations

6,489,607

Mined by

⛏️ .aR8Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

ed966a9406c64d4aafba045678c26adc679e17c9575beef59c4d6e7fd315ab86

Transactions (4)

Coinbase70bf2ed7a88991…5855e9f2049cfa

1 in → 28 out9.6600 XPM1015 B

Ad9pSzHt…cpJ3y2zz AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AJYusoxy…LtcN2Chh AbtgNzNb…9Atvu81w

79c404904a2f56…68643de4876743

1 in → 2 out3.5598 XPM225 B

AKBVYqzi…nLZz47rC AZjeddZV…Kh4AxMh5

4b35e0adea8914…0d4a328673f2ba

1 in → 2 out3.5027 XPM226 B

AakTYTYm…aXYmwgyQ AYXHwBtL…FcYgFqtP

661602bca582f2…87e3305642ebb4

2 in → 2 out1.3703 XPM373 B

ASHqWAYa…qiDQN2jG APsuxSWi…mmezoSD4

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.

6.231 × 10⁹⁸(99-digit number)

62316240320792496125…92058963151686759519

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

6.231 × 10⁹⁸(99-digit number)

62316240320792496125…92058963151686759519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.231 × 10⁹⁸(99-digit number)

62316240320792496125…92058963151686759521

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

1.246 × 10⁹⁹(100-digit number)

12463248064158499225…84117926303373519039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.246 × 10⁹⁹(100-digit number)

12463248064158499225…84117926303373519041

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

2.492 × 10⁹⁹(100-digit number)

24926496128316998450…68235852606747038079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.492 × 10⁹⁹(100-digit number)

24926496128316998450…68235852606747038081

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

4.985 × 10⁹⁹(100-digit number)

49852992256633996900…36471705213494076159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.985 × 10⁹⁹(100-digit number)

49852992256633996900…36471705213494076161

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

9.970 × 10⁹⁹(100-digit number)

99705984513267993800…72943410426988152319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.970 × 10⁹⁹(100-digit number)

99705984513267993800…72943410426988152321

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

Block #317,742

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