Block #2,279,031

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/2/2017, 9:05:55 AM · Difficulty 10.9559 · 4,552,261 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3130e351b84286d901626e6872a3127fe4ba42729793bc22a7b65589601f62b1

View on Chainz ↗

Height

#2,279,031

Difficulty

10.955856

Transactions

Size

429 B

Version

Bits

0af4b2ff

Nonce

393,445,982

Timestamp

9/2/2017, 9:05:55 AM

Confirmations

4,552,261

Mined by

⛏️ P2SHAXk97JBXFSWMMdfrjrfnM2fEUoJJ3Vv3Ks

Merkle Root

2908f3f7d186c3067e51d26f25c8778a99a59e97e61b8702c67113e78341a951

Transactions (2)

Coinbase73ca2f8419965f…886a1d732c4306

1 in → 1 out8.3300 XPM110 B

AXk97JBX…JJ3Vv3Ks

260986b9d11e35…cc3c65bfc35523

1 in → 2 out3163.6953 XPM227 B

AS8Swa5k…emSJQqiE AMsyySqX…2FcT8HBy

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.

1.232 × 10⁹⁹(100-digit number)

12320954726236158927…09744897254294159359

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

1.232 × 10⁹⁹(100-digit number)

12320954726236158927…09744897254294159359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.232 × 10⁹⁹(100-digit number)

12320954726236158927…09744897254294159361

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

2.464 × 10⁹⁹(100-digit number)

24641909452472317855…19489794508588318719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.464 × 10⁹⁹(100-digit number)

24641909452472317855…19489794508588318721

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

4.928 × 10⁹⁹(100-digit number)

49283818904944635711…38979589017176637439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.928 × 10⁹⁹(100-digit number)

49283818904944635711…38979589017176637441

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

9.856 × 10⁹⁹(100-digit number)

98567637809889271423…77959178034353274879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.856 × 10⁹⁹(100-digit number)

98567637809889271423…77959178034353274881

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

1.971 × 10¹⁰⁰(101-digit number)

19713527561977854284…55918356068706549759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.971 × 10¹⁰⁰(101-digit number)

19713527561977854284…55918356068706549761

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 #2,279,031

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