Block #320,433

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2013, 3:50:50 PM · Difficulty 10.1828 · 6,482,712 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e4f8f7fe3e2d711fdc9202bce5e8a8f606ccac1ae26ccb0a789549c48aaed1e5

View on Chainz ↗

Height

#320,433

Difficulty

10.182765

Transactions

Size

1.08 KB

Version

Bits

0a2ec9b2

Nonce

17,237

Timestamp

12/19/2013, 3:50:50 PM

Confirmations

6,482,712

Mined by

⛏️ aR4Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

d510e792c8fe7b8258890bc295d527ec1de657be3fdcd11c6f9a2b57081b7681

Transactions (1)

Coinbased510e792c8fe7b…9a2b57081b7681

1 in → 28 out9.6100 XPM1015 B

Aac9Hjdg…P4ktypc3 AZemWJAo…6jhDtieG AYtDvcGs…VuAcA7m7 AQwRN8bE…V8PsTcY9 AKzkYQaQ…zR4FspJZ

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.

5.825 × 10⁹⁷(98-digit number)

58259473961046349921…99967553976197821119

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

5.825 × 10⁹⁷(98-digit number)

58259473961046349921…99967553976197821119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.825 × 10⁹⁷(98-digit number)

58259473961046349921…99967553976197821121

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

1.165 × 10⁹⁸(99-digit number)

11651894792209269984…99935107952395642239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.165 × 10⁹⁸(99-digit number)

11651894792209269984…99935107952395642241

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

2.330 × 10⁹⁸(99-digit number)

23303789584418539968…99870215904791284479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.330 × 10⁹⁸(99-digit number)

23303789584418539968…99870215904791284481

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

4.660 × 10⁹⁸(99-digit number)

46607579168837079937…99740431809582568959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.660 × 10⁹⁸(99-digit number)

46607579168837079937…99740431809582568961

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

9.321 × 10⁹⁸(99-digit number)

93215158337674159874…99480863619165137919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.321 × 10⁹⁸(99-digit number)

93215158337674159874…99480863619165137921

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