Block #422,164

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 12:54:42 PM · Difficulty 10.3799 · 6,405,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65489214fb797595f0d3bd1d92f4b59199aafd47128a1094a6921a968bd4d98a

View on Chainz ↗

Height

#422,164

Difficulty

10.379896

Transactions

Size

991 B

Version

Bits

0a6140d9

Nonce

218,308

Timestamp

2/27/2014, 12:54:42 PM

Confirmations

6,405,131

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6800cccb55419e8b57016578bc01552261d22d5c54fe040ea536578946727c55

Transactions (4)

Coinbase3c44b0b0d4f4c1…b01b32d4f0ff14

1 in → 1 out9.3000 XPM110 B

AeKNrjNj…1NEq95Ta

5f930fb621bacd…f3a38464b2f25d

2 in → 1 out69.9900 XPM340 B

AVkR7Akb…gDKoKHLb

c343912aa70440…2772e5740b9cd5

1 in → 2 out7402.5344 XPM226 B

APhA4AUP…n5Cuv2LM AY4H42CP…4bQ4ZA3H

c4d41f2f04871f…80eb344e6cc788

1 in → 2 out1.1491 XPM226 B

AWyKEgjE…rwwHvZqh AYeiSWB3…xfPqVRcf

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.

1.145 × 10⁹²(93-digit number)

11456609397571612511…84294893169885764199

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

1.145 × 10⁹²(93-digit number)

11456609397571612511…84294893169885764199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.145 × 10⁹²(93-digit number)

11456609397571612511…84294893169885764201

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

2.291 × 10⁹²(93-digit number)

22913218795143225022…68589786339771528399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.291 × 10⁹²(93-digit number)

22913218795143225022…68589786339771528401

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

4.582 × 10⁹²(93-digit number)

45826437590286450045…37179572679543056799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.582 × 10⁹²(93-digit number)

45826437590286450045…37179572679543056801

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

9.165 × 10⁹²(93-digit number)

91652875180572900090…74359145359086113599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.165 × 10⁹²(93-digit number)

91652875180572900090…74359145359086113601

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

1.833 × 10⁹³(94-digit number)

18330575036114580018…48718290718172227199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.833 × 10⁹³(94-digit number)

18330575036114580018…48718290718172227201

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 #422,164

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