Block #2,304,273

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/22/2017, 3:41:31 AM · Difficulty 10.9175 · 4,537,191 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

420af12e93f1f7e6f7cdb3b956b7505605b9d47feb18aab071b8b0460c2bce5a

View on Chainz ↗

Height

#2,304,273

Difficulty

10.917478

Transactions

Size

872 B

Version

Bits

0aeadfd4

Nonce

1,850,592,649

Timestamp

9/22/2017, 3:41:31 AM

Confirmations

4,537,191

Mined by

⛏️ P2SHASWrFV4qqn62dcSNBrMGRpBvKeCksvHNL3

Merkle Root

1ba05e8cef19b7e12d9dbc03b1975a65d4234cda81ceffe924019137b00a608f

Transactions (2)

Coinbase6603408e8640f6…1f37b368b91e62

1 in → 1 out8.3900 XPM110 B

ASWrFV4q…CksvHNL3

3a659aff4d5352…959364514329e9

4 in → 2 out0.4145 XPM672 B

AUC5XRVY…Aq7vuTW2 AVJkDboV…YRZ8sG41

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.

1.619 × 10⁹⁵(96-digit number)

16191632309884556858…01619040978818232239

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

1.619 × 10⁹⁵(96-digit number)

16191632309884556858…01619040978818232239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.619 × 10⁹⁵(96-digit number)

16191632309884556858…01619040978818232241

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

3.238 × 10⁹⁵(96-digit number)

32383264619769113716…03238081957636464479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.238 × 10⁹⁵(96-digit number)

32383264619769113716…03238081957636464481

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

6.476 × 10⁹⁵(96-digit number)

64766529239538227433…06476163915272928959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.476 × 10⁹⁵(96-digit number)

64766529239538227433…06476163915272928961

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

1.295 × 10⁹⁶(97-digit number)

12953305847907645486…12952327830545857919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.295 × 10⁹⁶(97-digit number)

12953305847907645486…12952327830545857921

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

2.590 × 10⁹⁶(97-digit number)

25906611695815290973…25904655661091715839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.590 × 10⁹⁶(97-digit number)

25906611695815290973…25904655661091715841

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 #2,304,273

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