Block #2,130,324

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2017, 8:48:31 AM · Difficulty 10.9094 · 4,701,504 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7e2599cd1c81900b9e4ff83fa3063be4989f5ee5f19836a5f3c63b0619d6b306

View on Chainz ↗

Height

#2,130,324

Difficulty

10.909370

Transactions

Size

424 B

Version

Bits

0ae8cc76

Nonce

240,095,931

Timestamp

5/24/2017, 8:48:31 AM

Confirmations

4,701,504

Mined by

⛏️ P2SHAYnSuthEMJkjkQY6QxATNHFEBw3kphvUfp

Merkle Root

07b53509edd126e4fc97bd169dada1deec055e7b0b08393ce4ab077a835ae4a1

Transactions (2)

Coinbase105f0c940d906a…bc9221599bd6d4

1 in → 1 out8.4000 XPM110 B

AYnSuthE…3kphvUfp

004af7f6f72b41…416ed9a37947e7

1 in → 2 out114434.1624 XPM225 B

AJ38s7j1…osygnxMd ATNNwPCV…id21vw5x

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.

4.254 × 10⁹²(93-digit number)

42549062503065011639…11698059571140398439

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

4.254 × 10⁹²(93-digit number)

42549062503065011639…11698059571140398439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.254 × 10⁹²(93-digit number)

42549062503065011639…11698059571140398441

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

8.509 × 10⁹²(93-digit number)

85098125006130023278…23396119142280796879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.509 × 10⁹²(93-digit number)

85098125006130023278…23396119142280796881

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

1.701 × 10⁹³(94-digit number)

17019625001226004655…46792238284561593759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.701 × 10⁹³(94-digit number)

17019625001226004655…46792238284561593761

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

3.403 × 10⁹³(94-digit number)

34039250002452009311…93584476569123187519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.403 × 10⁹³(94-digit number)

34039250002452009311…93584476569123187521

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

6.807 × 10⁹³(94-digit number)

68078500004904018622…87168953138246375039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.807 × 10⁹³(94-digit number)

68078500004904018622…87168953138246375041

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 #2,130,324

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