Block #114,966

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/13/2013, 11:52:28 AM · Difficulty 9.7413 · 6,711,874 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8c977e9c5758d4ed7013ca82f8aa479d82103a849132af58d3ec8e31bdc71dbd

View on Chainz ↗

Height

#114,966

Difficulty

9.741289

Transactions

Size

1.14 KB

Version

Bits

09bdc51b

Nonce

48,435

Timestamp

8/13/2013, 11:52:28 AM

Confirmations

6,711,874

Mined by

⛏️ P2SHAb7gaYcUerg2muYXSr7AXqsVVYcr8EYTqP

Merkle Root

f4ea9df6461bcb8fe8ba7d3476eff41c1542c87145756067f43d621f196ea65e

Transactions (2)

Coinbase3d4de72915ba3d…cbf49bed37f8b3

1 in → 1 out10.5300 XPM109 B

Ab7gaYcU…cr8EYTqP

c96fe4cbac7e6e…84ac909d17de37

6 in → 2 out2.0257 XPM964 B

ATasJjrv…VYGJy5QS ATmbQxcW…5qEcMtPu

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.

6.187 × 10⁹⁴(95-digit number)

61874395347564055020…52132840600496711849

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

6.187 × 10⁹⁴(95-digit number)

61874395347564055020…52132840600496711849

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.187 × 10⁹⁴(95-digit number)

61874395347564055020…52132840600496711851

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

1.237 × 10⁹⁵(96-digit number)

12374879069512811004…04265681200993423699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.237 × 10⁹⁵(96-digit number)

12374879069512811004…04265681200993423701

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

2.474 × 10⁹⁵(96-digit number)

24749758139025622008…08531362401986847399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.474 × 10⁹⁵(96-digit number)

24749758139025622008…08531362401986847401

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

4.949 × 10⁹⁵(96-digit number)

49499516278051244016…17062724803973694799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.949 × 10⁹⁵(96-digit number)

49499516278051244016…17062724803973694801

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

9.899 × 10⁹⁵(96-digit number)

98999032556102488032…34125449607947389599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.899 × 10⁹⁵(96-digit number)

98999032556102488032…34125449607947389601

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 #114,966

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