Block #222,480

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/22/2013, 6:42:22 AM · Difficulty 9.9394 · 6,573,862 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d550d1ece0bd508ec38ba568630deb1cf8b9a25f65a27775158a796b9033248

View on Chainz ↗

Height

#222,480

Difficulty

9.939406

Transactions

Size

1.24 KB

Version

Bits

09f07ce4

Nonce

3,414

Timestamp

10/22/2013, 6:42:22 AM

Confirmations

6,573,862

Mined by

⛏️ eRfAJaGRnajU4FKPNSjrHvpAByLABiCHGoy6E

Merkle Root

2b728e1e2a758c564d87d8d26572558d43ee0c48e77a112ab40bd4d242efc690

Transactions (1)

Coinbase2b728e1e2a758c…0bd4d242efc690

1 in → 33 out10.0900 XPM1.16 KB

AJaGRnaj…iCHGoy6E AUmqvzVP…R7Pd9B3z Ab3dSvM7…Qoxxb9tp ARg8Kp4c…n7AUWZXy AKDTDDtx…iqvw9cdY

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.

4.373 × 10⁹⁵(96-digit number)

43733454490690991142…75789744648172256799

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

4.373 × 10⁹⁵(96-digit number)

43733454490690991142…75789744648172256799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.373 × 10⁹⁵(96-digit number)

43733454490690991142…75789744648172256801

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

8.746 × 10⁹⁵(96-digit number)

87466908981381982285…51579489296344513599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.746 × 10⁹⁵(96-digit number)

87466908981381982285…51579489296344513601

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

1.749 × 10⁹⁶(97-digit number)

17493381796276396457…03158978592689027199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.749 × 10⁹⁶(97-digit number)

17493381796276396457…03158978592689027201

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

3.498 × 10⁹⁶(97-digit number)

34986763592552792914…06317957185378054399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.498 × 10⁹⁶(97-digit number)

34986763592552792914…06317957185378054401

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

6.997 × 10⁹⁶(97-digit number)

69973527185105585828…12635914370756108799

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