Block #355,279

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 1:22:01 AM · Difficulty 10.3583 · 6,440,736 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ce96c014b061f4370133d6b1521cc073572c073801c110e14b4808cdb4d1801

View on Chainz ↗

Height

#355,279

Difficulty

10.358346

Transactions

Size

3.17 KB

Version

Bits

0a5bbc93

Nonce

26,316

Timestamp

1/12/2014, 1:22:01 AM

Confirmations

6,440,736

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6a0d1b509aaf741efdbe74fb73e4c0a26510105865f64e94b6123a4a6bd7f288

Transactions (4)

Coinbase4e3c2c6765bca6…187a23f1b1f114

1 in → 1 out9.3600 XPM110 B

AeKNrjNj…1NEq95Ta

1b2cf074ef9ba7…45a679f428ccdc

15 in → 2 out15.3980 XPM2.24 KB

ANQVP39c…tZnYzpAH AGF7RX5K…VRz4NRX4

de655d9b3dd865…13afff4fca8e61

3 in → 2 out3.2069 XPM522 B

Aekhe77V…VLGVQgMs ASDTZPnu…3J2vfGPJ

6a75349f8bf44c…a68e9461560b27

1 in → 2 out2.2042 XPM226 B

AZ4x2btP…9auP3DZ8 AeiESozR…BUnpTCDK

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.

5.728 × 10⁹⁹(100-digit number)

57288025810133943403…96449896889530701119

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

5.728 × 10⁹⁹(100-digit number)

57288025810133943403…96449896889530701119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.728 × 10⁹⁹(100-digit number)

57288025810133943403…96449896889530701121

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

1.145 × 10¹⁰⁰(101-digit number)

11457605162026788680…92899793779061402239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.145 × 10¹⁰⁰(101-digit number)

11457605162026788680…92899793779061402241

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

2.291 × 10¹⁰⁰(101-digit number)

22915210324053577361…85799587558122804479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.291 × 10¹⁰⁰(101-digit number)

22915210324053577361…85799587558122804481

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

4.583 × 10¹⁰⁰(101-digit number)

45830420648107154722…71599175116245608959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.583 × 10¹⁰⁰(101-digit number)

45830420648107154722…71599175116245608961

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

9.166 × 10¹⁰⁰(101-digit number)

91660841296214309445…43198350232491217919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.166 × 10¹⁰⁰(101-digit number)

91660841296214309445…43198350232491217921

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