Block #418,133

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/24/2014, 3:16:41 PM · Difficulty 10.3961 · 6,385,161 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de804e246756cb663322e3eb54447f4177c3b8cfd3c8443de07d17e94871050e

View on Chainz ↗

Height

#418,133

Difficulty

10.396137

Transactions

Size

1.38 KB

Version

Bits

0a656936

Nonce

396,215

Timestamp

2/24/2014, 3:16:41 PM

Confirmations

6,385,161

Mined by

⛏️ UaAcuM7XiJ6QSTDXS73zz3uhVx2G5uND8Jce

Merkle Root

45d74b82f2ec5d0972046000ff56b4bf310431b90a8ef16c9c074081dce3ea56

Transactions (2)

Coinbase3f4f6928f80137…8b21d1cb3362c4

1 in → 24 out9.2500 XPM879 B

AcuM7XiJ…5uND8Jce AVRMvm7T…6PC6keBx AZqjMFvv…G8aw2zC8 AGz9gyZW…bo8NYQpw Acs9SHrk…QJSB8SFG

0edc8aa302a73c…380c21a0a073dd

2 in → 5 out13.0195 XPM442 B

AeKNrjNj…1NEq95Ta AbBfJxdv…5LhhDvme AJyGidYK…wD9VP2WE AJm7Bato…CGjsUjn8 APRxG4Vc…GZqmXrSs

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.

4.940 × 10⁹⁶(97-digit number)

49407957283463163207…80756391221799885349

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

4.940 × 10⁹⁶(97-digit number)

49407957283463163207…80756391221799885349

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.940 × 10⁹⁶(97-digit number)

49407957283463163207…80756391221799885351

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

9.881 × 10⁹⁶(97-digit number)

98815914566926326415…61512782443599770699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.881 × 10⁹⁶(97-digit number)

98815914566926326415…61512782443599770701

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

1.976 × 10⁹⁷(98-digit number)

19763182913385265283…23025564887199541399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.976 × 10⁹⁷(98-digit number)

19763182913385265283…23025564887199541401

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

3.952 × 10⁹⁷(98-digit number)

39526365826770530566…46051129774399082799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.952 × 10⁹⁷(98-digit number)

39526365826770530566…46051129774399082801

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

7.905 × 10⁹⁷(98-digit number)

79052731653541061132…92102259548798165599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.905 × 10⁹⁷(98-digit number)

79052731653541061132…92102259548798165601

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