Block #363,866

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/17/2014, 5:01:36 PM · Difficulty 10.4163 · 6,428,898 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8f550f4319e7913b064c0bb22247b1f2d5b36dc219660a1f57d253a589de7f5b

View on Chainz ↗

Height

#363,866

Difficulty

10.416289

Transactions

Size

417 B

Version

Bits

0a6a91ed

Nonce

66,867

Timestamp

1/17/2014, 5:01:36 PM

Confirmations

6,428,898

Merkle Root

3b466d46372cf78e034e77b5b65c1f7a7305b47397732b3c946dd39b7068bca7

Transactions (2)

Coinbase21ef485c534bab…e78d39013b6b59

1 in → 1 out9.2100 XPM100 B

AaXb6Ldz…XefG91jF

7e3c10d5d52be7…f6c3b2117f7081

1 in → 2 out2.0526 XPM225 B

AT4ma7Hq…bgqUfkJN Accdt3jt…s9BSMy7i

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.

2.886 × 10⁹⁸(99-digit number)

28860050494570026379…40424322220168501299

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

2.886 × 10⁹⁸(99-digit number)

28860050494570026379…40424322220168501299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.886 × 10⁹⁸(99-digit number)

28860050494570026379…40424322220168501301

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

5.772 × 10⁹⁸(99-digit number)

57720100989140052759…80848644440337002599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.772 × 10⁹⁸(99-digit number)

57720100989140052759…80848644440337002601

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

1.154 × 10⁹⁹(100-digit number)

11544020197828010551…61697288880674005199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.154 × 10⁹⁹(100-digit number)

11544020197828010551…61697288880674005201

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

2.308 × 10⁹⁹(100-digit number)

23088040395656021103…23394577761348010399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.308 × 10⁹⁹(100-digit number)

23088040395656021103…23394577761348010401

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

4.617 × 10⁹⁹(100-digit number)

46176080791312042207…46789155522696020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.617 × 10⁹⁹(100-digit number)

46176080791312042207…46789155522696020801

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