Block #404,948

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2014, 6:08:07 AM · Difficulty 10.4269 · 6,394,226 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e52f3070c513765ca6b828c899fadc4ae6dbec1c3a3ec6f89cef7249a5d13996

View on Chainz ↗

Height

#404,948

Difficulty

10.426913

Transactions

Size

859 B

Version

Bits

0a6d4a30

Nonce

188,844

Timestamp

2/15/2014, 6:08:07 AM

Confirmations

6,394,226

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

8bd03e36a6de4a0165a3a4b19c71cbf5aba44492b230c696f3064d403250a1fc

Transactions (2)

Coinbase3f03bdfb446f93…6eb55ced077ddd

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

986082c0ae4d9f…6bc5fd77af0cd6

3 in → 9 out27.5600 XPM659 B

AdwYsaaT…D6SV1XP6 AeKNrjNj…1NEq95Ta AJaQENaD…wRN4nbo6 Ab5fvUgL…VFyiRgEh ASNne1ZG…gbPeahqt

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.

9.661 × 10⁹⁵(96-digit number)

96615129215412202347…60926643327387776879

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

9.661 × 10⁹⁵(96-digit number)

96615129215412202347…60926643327387776879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.661 × 10⁹⁵(96-digit number)

96615129215412202347…60926643327387776881

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

1.932 × 10⁹⁶(97-digit number)

19323025843082440469…21853286654775553759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.932 × 10⁹⁶(97-digit number)

19323025843082440469…21853286654775553761

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

3.864 × 10⁹⁶(97-digit number)

38646051686164880938…43706573309551107519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.864 × 10⁹⁶(97-digit number)

38646051686164880938…43706573309551107521

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

7.729 × 10⁹⁶(97-digit number)

77292103372329761877…87413146619102215039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.729 × 10⁹⁶(97-digit number)

77292103372329761877…87413146619102215041

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

1.545 × 10⁹⁷(98-digit number)

15458420674465952375…74826293238204430079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.545 × 10⁹⁷(98-digit number)

15458420674465952375…74826293238204430081

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