Block #2,267,314

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/25/2017, 12:42:32 PM · Difficulty 10.9517 · 4,566,099 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

63a4fb1e3cdcb535add82c0c763f9874d163169f62a561f8e15e02933569e90d

View on Chainz ↗

Height

#2,267,314

Difficulty

10.951695

Transactions

Size

1.22 KB

Version

Bits

0af3a249

Nonce

6,665,644

Timestamp

8/25/2017, 12:42:32 PM

Confirmations

4,566,099

Mined by

⛏️ P2SHAQQ9uiqAwQnBFDdSHH6izRYWXRWbn3HRdy

Merkle Root

c17261a2aa08f8d034a363805dad9f4aa0db123a688babc6fd15723568500e1c

Transactions (3)

Coinbase533cff899a9d5b…6e1e257065bf02

1 in → 1 out8.3500 XPM110 B

AQQ9uiqA…Wbn3HRdy

44bb09577e9beb…f37842ad4bdb2d

5 in → 2 out773.4142 XPM818 B

ALfb3AgN…gyt3DNb1 AZMe9Hpi…mvFNEcJ5

5ec8b2a2c08785…b671bee057f2bc

1 in → 2 out36048.2186 XPM227 B

AZdWWKhs…UidBDSmX ASp9ADgk…otv74BQa

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.

1.429 × 10⁹⁶(97-digit number)

14295112892025256757…69053634879099796479

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

1.429 × 10⁹⁶(97-digit number)

14295112892025256757…69053634879099796479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.429 × 10⁹⁶(97-digit number)

14295112892025256757…69053634879099796481

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

2.859 × 10⁹⁶(97-digit number)

28590225784050513514…38107269758199592959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.859 × 10⁹⁶(97-digit number)

28590225784050513514…38107269758199592961

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

5.718 × 10⁹⁶(97-digit number)

57180451568101027029…76214539516399185919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.718 × 10⁹⁶(97-digit number)

57180451568101027029…76214539516399185921

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

1.143 × 10⁹⁷(98-digit number)

11436090313620205405…52429079032798371839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.143 × 10⁹⁷(98-digit number)

11436090313620205405…52429079032798371841

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

2.287 × 10⁹⁷(98-digit number)

22872180627240410811…04858158065596743679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.287 × 10⁹⁷(98-digit number)

22872180627240410811…04858158065596743681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.574 × 10⁹⁷(98-digit number)

45744361254480821623…09716316131193487359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,267,314

Cookie Preferences