Block #301,288

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/9/2013, 2:47:00 AM · Difficulty 9.9925 · 6,516,645 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

476c816ac82bc9829353d24f8d62fbdc62aca564b0d39498510f584e56005e80

View on Chainz ↗

Height

#301,288

Difficulty

9.992486

Transactions

Size

1.11 KB

Version

Bits

09fe1394

Nonce

80,103

Timestamp

12/9/2013, 2:47:00 AM

Confirmations

6,516,645

Mined by

⛏️ aR.CAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

188afe3feb5b2657de2c5c9143589e5f90ac4877ebf36797f7949bfd787121ab

Transactions (1)

Coinbase188afe3feb5b26…949bfd787121ab

1 in → 29 out9.9800 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz Acs9SHrk…QJSB8SFG AHjxjypg…BfqPH2LH APeshfYV…3PKcKMKH 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.

6.735 × 10⁹⁶(97-digit number)

67358804766485829170…91919504606158669239

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

6.735 × 10⁹⁶(97-digit number)

67358804766485829170…91919504606158669239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.735 × 10⁹⁶(97-digit number)

67358804766485829170…91919504606158669241

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

1.347 × 10⁹⁷(98-digit number)

13471760953297165834…83839009212317338479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.347 × 10⁹⁷(98-digit number)

13471760953297165834…83839009212317338481

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

2.694 × 10⁹⁷(98-digit number)

26943521906594331668…67678018424634676959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.694 × 10⁹⁷(98-digit number)

26943521906594331668…67678018424634676961

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

5.388 × 10⁹⁷(98-digit number)

53887043813188663336…35356036849269353919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.388 × 10⁹⁷(98-digit number)

53887043813188663336…35356036849269353921

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

1.077 × 10⁹⁸(99-digit number)

10777408762637732667…70712073698538707839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #301,288

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