Block #222,411

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/22/2013, 5:35:33 AM · Difficulty 9.9394 · 6,586,455 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d22ab8d3d85a620eaa52334e5c05c370d4672d74b6207a1113f92b9b6b53b111

View on Chainz ↗

Height

#222,411

Difficulty

9.939412

Transactions

Size

1.18 KB

Version

Bits

09f07d4c

Nonce

328,293

Timestamp

10/22/2013, 5:35:33 AM

Confirmations

6,586,455

Mined by

⛏️ dRfAS6sRu1RZyNqYNxz1pTq4rDhZ6UpJKwm5m

Merkle Root

0926b229ed45344804f4e18e12462df6d46590b18e1438e0ba27d31ae7cac0b3

Transactions (1)

Coinbase0926b229ed4534…27d31ae7cac0b3

1 in → 31 out10.0900 XPM1.09 KB

AS6sRu1R…UpJKwm5m AUT1qxTx…t5B3qd8Z AduWjQsS…QvBAAhCq AWCfnjpk…hb1ovL8F APms8CCz…ozExfdFt

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.

4.058 × 10⁹¹(92-digit number)

40583462574326672105…46113127200446297599

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

4.058 × 10⁹¹(92-digit number)

40583462574326672105…46113127200446297599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.058 × 10⁹¹(92-digit number)

40583462574326672105…46113127200446297601

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

8.116 × 10⁹¹(92-digit number)

81166925148653344211…92226254400892595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.116 × 10⁹¹(92-digit number)

81166925148653344211…92226254400892595201

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

1.623 × 10⁹²(93-digit number)

16233385029730668842…84452508801785190399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.623 × 10⁹²(93-digit number)

16233385029730668842…84452508801785190401

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

3.246 × 10⁹²(93-digit number)

32466770059461337684…68905017603570380799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.246 × 10⁹²(93-digit number)

32466770059461337684…68905017603570380801

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

6.493 × 10⁹²(93-digit number)

64933540118922675369…37810035207140761599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #222,411

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