Block #2,315,894

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/30/2017, 2:45:59 PM · Difficulty 10.9081 · 4,525,570 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bd8832db7738e57661e5ba5db8a85b233e67e8a4b9ff8ece43fdd651d7536278

View on Chainz ↗

Height

#2,315,894

Difficulty

10.908060

Transactions

Size

1.72 KB

Version

Bits

0ae8769b

Nonce

1,889,999,632

Timestamp

9/30/2017, 2:45:59 PM

Confirmations

4,525,570

Mined by

⛏️ P2SHAdBRUDS6fAJHnRzkoiMwhWWuGdgPzXqhdd

Merkle Root

6e44c4a137efdfba60de4f278fbf720f718baf2a95fd0d63be443b4739a1dc83

Transactions (2)

Coinbase68da2caea2b7a4…2c00e56687e2fc

1 in → 1 out8.4100 XPM109 B

AdBRUDS6…gPzXqhdd

4d2a588478e44a…252670d7f9a834

10 in → 2 out108.0991 XPM1.53 KB

Ac4TAbrE…bDdiQ2NG AXiUgzzB…5zUEiem2

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.

1.325 × 10⁹⁶(97-digit number)

13254447151689288734…92886614166631219199

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

1.325 × 10⁹⁶(97-digit number)

13254447151689288734…92886614166631219199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.325 × 10⁹⁶(97-digit number)

13254447151689288734…92886614166631219201

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

2.650 × 10⁹⁶(97-digit number)

26508894303378577469…85773228333262438399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.650 × 10⁹⁶(97-digit number)

26508894303378577469…85773228333262438401

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

5.301 × 10⁹⁶(97-digit number)

53017788606757154938…71546456666524876799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.301 × 10⁹⁶(97-digit number)

53017788606757154938…71546456666524876801

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

1.060 × 10⁹⁷(98-digit number)

10603557721351430987…43092913333049753599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.060 × 10⁹⁷(98-digit number)

10603557721351430987…43092913333049753601

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

2.120 × 10⁹⁷(98-digit number)

21207115442702861975…86185826666099507199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.120 × 10⁹⁷(98-digit number)

21207115442702861975…86185826666099507201

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 #2,315,894

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