Block #2,442,610

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/26/2017, 4:59:43 PM · Difficulty 10.9318 · 4,396,916 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ba68e804de77e5dc5f6abc6a182ebdfbc59227d46a8895be52ed4205ac531e6c

View on Chainz ↗

Height

#2,442,610

Difficulty

10.931842

Transactions

Size

3.45 KB

Version

Bits

0aee8d2f

Nonce

1,703,708,370

Timestamp

12/26/2017, 4:59:43 PM

Confirmations

4,396,916

Mined by

⛏️ P2SHAUhMzaEafeKcrN12tJYMEqjmBZ2vjnqpTs

Merkle Root

1c589391143b9633424ccaf3df0e658265b3d6562a43ee07729ca0708b1b8512

Transactions (2)

Coinbase1c0bca4e75e1e2…5bf09a9222047f

1 in → 1 out8.3900 XPM109 B

AUhMzaEa…2vjnqpTs

f8438fb64d0ac8…9a4525a7bb4c6a

22 in → 2 out370.3825 XPM3.25 KB

AaS6FZNA…q7CSAkWX AdWNahYS…codohPEh

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.

2.293 × 10⁹⁷(98-digit number)

22934943939017834489…25037279002121994239

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

2.293 × 10⁹⁷(98-digit number)

22934943939017834489…25037279002121994239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.293 × 10⁹⁷(98-digit number)

22934943939017834489…25037279002121994241

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

4.586 × 10⁹⁷(98-digit number)

45869887878035668978…50074558004243988479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.586 × 10⁹⁷(98-digit number)

45869887878035668978…50074558004243988481

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

9.173 × 10⁹⁷(98-digit number)

91739775756071337956…00149116008487976959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.173 × 10⁹⁷(98-digit number)

91739775756071337956…00149116008487976961

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

1.834 × 10⁹⁸(99-digit number)

18347955151214267591…00298232016975953919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.834 × 10⁹⁸(99-digit number)

18347955151214267591…00298232016975953921

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

3.669 × 10⁹⁸(99-digit number)

36695910302428535182…00596464033951907839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.669 × 10⁹⁸(99-digit number)

36695910302428535182…00596464033951907841

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 #2,442,610

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