Block #303,595

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 11:27:13 AM · Difficulty 9.9931 · 6,503,479 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1987bf2dd5e78e618c322513e85932ed0dbfabf81769e19a6d44a7af946b7939

View on Chainz ↗

Height

#303,595

Difficulty

9.993055

Transactions

Size

1.14 KB

Version

Bits

09fe38db

Nonce

258,934

Timestamp

12/10/2013, 11:27:13 AM

Confirmations

6,503,479

Mined by

⛏️ aRHTAcskt6D1qHZM6az3n2o97GmPByDb4ci1L8

Merkle Root

0e6bedb3911b9701a02d2cf029164c893295fa7f229ea5c1dd22f09964839732

Transactions (1)

Coinbase0e6bedb3911b97…22f09964839732

1 in → 30 out9.9800 XPM1.06 KB

Acskt6D1…Db4ci1L8 Ad9pSzHt…cpJ3y2zz AJjsX4t4…gtmJp9SX AWZd1qVJ…9pj9yfPa Acs9SHrk…QJSB8SFG

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.

3.407 × 10⁸⁹(90-digit number)

34075654257869990611…88153514195335854479

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

3.407 × 10⁸⁹(90-digit number)

34075654257869990611…88153514195335854479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.407 × 10⁸⁹(90-digit number)

34075654257869990611…88153514195335854481

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

6.815 × 10⁸⁹(90-digit number)

68151308515739981222…76307028390671708959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.815 × 10⁸⁹(90-digit number)

68151308515739981222…76307028390671708961

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

1.363 × 10⁹⁰(91-digit number)

13630261703147996244…52614056781343417919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.363 × 10⁹⁰(91-digit number)

13630261703147996244…52614056781343417921

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

2.726 × 10⁹⁰(91-digit number)

27260523406295992489…05228113562686835839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.726 × 10⁹⁰(91-digit number)

27260523406295992489…05228113562686835841

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

5.452 × 10⁹⁰(91-digit number)

54521046812591984978…10456227125373671679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.452 × 10⁹⁰(91-digit number)

54521046812591984978…10456227125373671681

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 #303,595

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