Block #462,561

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 12:46:38 PM · Difficulty 10.4134 · 6,348,280 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

715dea1d4a23fab105f163fdc90b138a33c5d4e8ecd01010d333b6dcb9e15079

View on Chainz ↗

Height

#462,561

Difficulty

10.413382

Transactions

Size

4.53 KB

Version

Bits

0a69d36a

Nonce

90,690

Timestamp

3/27/2014, 12:46:38 PM

Confirmations

6,348,280

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

eebaa6b1f7f36f9ab3ca00297ee6bb7d0ae1a57eff47bce0e566e24330fdc893

Transactions (2)

Coinbase793e56506a33a2…fce7761d5c9a76

1 in → 3 out9.2600 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

a0f8927e34f387…049cda2292db98

16 in → 59 out147.1800 XPM4.28 KB

AZv29ja6…trEEibF5 ARapidPq…BD8pNF5M Af1Eejkx…cKmYn3YE AUkdqaxr…4jcbMUQ7 APSoHXZY…kNZx697r

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.

7.602 × 10⁹⁵(96-digit number)

76022919103891872214…69290703788101473279

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

7.602 × 10⁹⁵(96-digit number)

76022919103891872214…69290703788101473279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.602 × 10⁹⁵(96-digit number)

76022919103891872214…69290703788101473281

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

1.520 × 10⁹⁶(97-digit number)

15204583820778374442…38581407576202946559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.520 × 10⁹⁶(97-digit number)

15204583820778374442…38581407576202946561

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

3.040 × 10⁹⁶(97-digit number)

30409167641556748885…77162815152405893119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.040 × 10⁹⁶(97-digit number)

30409167641556748885…77162815152405893121

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

6.081 × 10⁹⁶(97-digit number)

60818335283113497771…54325630304811786239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.081 × 10⁹⁶(97-digit number)

60818335283113497771…54325630304811786241

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

1.216 × 10⁹⁷(98-digit number)

12163667056622699554…08651260609623572479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.216 × 10⁹⁷(98-digit number)

12163667056622699554…08651260609623572481

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 #462,561

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