Block #391

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/7/2013, 11:57:01 PM · Difficulty 7.0133 · 6,792,349 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84a4373b1f263824cef670c2cfc38390f163e92d008f8e0bd68cc8c0e039d22a

View on Chainz ↗

Height

#391

Difficulty

7.013270

Transactions

Size

199 B

Version

Bits

070365a8

Nonce

325

Timestamp

7/7/2013, 11:57:01 PM

Confirmations

6,792,349

Merkle Root

3d7e77c2213dc963cab97bf9789b23bf5c8fefd21f980f3790b989cc0b95e12f

Transactions (1)

Coinbase3d7e77c2213dc9…b989cc0b95e12f

1 in → 1 out20.3100 XPM108 B

AGpLwH35…gWJu3vdc

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.

1.159 × 10⁹⁸(99-digit number)

11593973245984668829…52047090041407536649

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

1.159 × 10⁹⁸(99-digit number)

11593973245984668829…52047090041407536649

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.159 × 10⁹⁸(99-digit number)

11593973245984668829…52047090041407536651

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

2.318 × 10⁹⁸(99-digit number)

23187946491969337659…04094180082815073299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.318 × 10⁹⁸(99-digit number)

23187946491969337659…04094180082815073301

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

4.637 × 10⁹⁸(99-digit number)

46375892983938675319…08188360165630146599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.637 × 10⁹⁸(99-digit number)

46375892983938675319…08188360165630146601

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

9.275 × 10⁹⁸(99-digit number)

92751785967877350638…16376720331260293199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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