Block #114,910

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/13/2013, 10:56:27 AM · Difficulty 9.7414 · 6,680,992 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a554270a276c83eac3932a6d777abda6f2b8bc5530ad071fe800f1a431fe489b

View on Chainz ↗

Height

#114,910

Difficulty

9.741364

Transactions

Size

1.37 KB

Version

Bits

09bdca0e

Nonce

45,562

Timestamp

8/13/2013, 10:56:27 AM

Confirmations

6,680,992

Mined by

⛏️ P2SHAeDRRCyHn8DYSDTfxpasX8AcS6shkxVACC

Merkle Root

b76b2e8a9a2a25ff0059d55b74948c7313d2fcf6ce32efdd8e87b7a5fd68c2ed

Transactions (4)

Coinbase7d9081244193af…485af770ac2305

1 in → 1 out10.5568 XPM109 B

AeDRRCyH…shkxVACC

f56ff9a7c7b18e…ff97904127b894

3 in → 2 out19.9572 XPM522 B

AcWNpkXk…cRTM3N8y ASiNpi6R…xU2JjyYm

c27b638e43c6be…2e6c831799b81b

3 in → 1 out15.1100 XPM488 B

AVbUYygu…86BSkU3f

8b8ed27fccb04c…79080e2c32c6e8

1 in → 1 out1.9919 XPM193 B

AKjsjTkW…7rGbLvxN

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.

3.656 × 10⁹⁶(97-digit number)

36567351614802137243…13842639695458525429

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

3.656 × 10⁹⁶(97-digit number)

36567351614802137243…13842639695458525429

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.656 × 10⁹⁶(97-digit number)

36567351614802137243…13842639695458525431

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

7.313 × 10⁹⁶(97-digit number)

73134703229604274487…27685279390917050859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.313 × 10⁹⁶(97-digit number)

73134703229604274487…27685279390917050861

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

1.462 × 10⁹⁷(98-digit number)

14626940645920854897…55370558781834101719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.462 × 10⁹⁷(98-digit number)

14626940645920854897…55370558781834101721

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

2.925 × 10⁹⁷(98-digit number)

29253881291841709795…10741117563668203439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.925 × 10⁹⁷(98-digit number)

29253881291841709795…10741117563668203441

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

5.850 × 10⁹⁷(98-digit number)

58507762583683419590…21482235127336406879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.850 × 10⁹⁷(98-digit number)

58507762583683419590…21482235127336406881

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