Block #314,532

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 12:39:00 AM · Difficulty 10.0654 · 6,496,067 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef9e74f9bf06ea2b4eb2510050034dcc3eeae787d90efa986da5bd23cc7650f1

View on Chainz ↗

Height

#314,532

Difficulty

10.065357

Transactions

Size

1.05 KB

Version

Bits

0a10bb42

Nonce

309,485

Timestamp

12/16/2013, 12:39:00 AM

Confirmations

6,496,067

Mined by

⛏️ aRKAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

fc458e7543d090317473a747083df4a5a66e7f8a2c3b1514ffc2aae1d1f7a202

Transactions (1)

Coinbasefc458e7543d090…c2aae1d1f7a202

1 in → 27 out9.8600 XPM981 B

Aac9Hjdg…P4ktypc3 AbtgNzNb…9Atvu81w Ad9pSzHt…cpJ3y2zz AQzPPdhT…gP6nfcp3 AKwqFUdz…D4jGNKFN

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.

3.805 × 10⁹⁴(95-digit number)

38057481875408301948…63646233692622503359

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

3.805 × 10⁹⁴(95-digit number)

38057481875408301948…63646233692622503359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.805 × 10⁹⁴(95-digit number)

38057481875408301948…63646233692622503361

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

7.611 × 10⁹⁴(95-digit number)

76114963750816603897…27292467385245006719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.611 × 10⁹⁴(95-digit number)

76114963750816603897…27292467385245006721

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

1.522 × 10⁹⁵(96-digit number)

15222992750163320779…54584934770490013439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.522 × 10⁹⁵(96-digit number)

15222992750163320779…54584934770490013441

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

3.044 × 10⁹⁵(96-digit number)

30445985500326641558…09169869540980026879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.044 × 10⁹⁵(96-digit number)

30445985500326641558…09169869540980026881

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

6.089 × 10⁹⁵(96-digit number)

60891971000653283117…18339739081960053759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.089 × 10⁹⁵(96-digit number)

60891971000653283117…18339739081960053761

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 #314,532

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