Block #386,814

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2014, 5:15:28 PM · Difficulty 10.4112 · 6,423,509 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

046d851562ac7df92f39391b21334b2f184f230100a1ac8509fb8d34887aa63b

View on Chainz ↗

Height

#386,814

Difficulty

10.411217

Transactions

Size

1.10 KB

Version

Bits

0a69458a

Nonce

8,042

Timestamp

2/2/2014, 5:15:28 PM

Confirmations

6,423,509

Mined by

⛏️ aR}AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

6c230ef6e4e3eb83c8ac378b8beb0a09d82083f377951c9bab8ffd2856263669

Transactions (2)

Coinbase11e6417436a2f3…e420aeffc3e0a8

1 in → 21 out9.2100 XPM777 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

212b2b8ef44723…211fbf9cc665ec

1 in → 3 out1.0050 XPM261 B

AccYkoBT…t5VvVcZk AbyekbUs…jrhybUkS AXxBeg5w…2EYyvzpV

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.

3.080 × 10⁹⁴(95-digit number)

30806259014666780791…04897058746086156799

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

3.080 × 10⁹⁴(95-digit number)

30806259014666780791…04897058746086156799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.080 × 10⁹⁴(95-digit number)

30806259014666780791…04897058746086156801

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

6.161 × 10⁹⁴(95-digit number)

61612518029333561582…09794117492172313599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.161 × 10⁹⁴(95-digit number)

61612518029333561582…09794117492172313601

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

1.232 × 10⁹⁵(96-digit number)

12322503605866712316…19588234984344627199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.232 × 10⁹⁵(96-digit number)

12322503605866712316…19588234984344627201

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

2.464 × 10⁹⁵(96-digit number)

24645007211733424632…39176469968689254399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.464 × 10⁹⁵(96-digit number)

24645007211733424632…39176469968689254401

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

4.929 × 10⁹⁵(96-digit number)

49290014423466849265…78352939937378508799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.929 × 10⁹⁵(96-digit number)

49290014423466849265…78352939937378508801

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 #386,814

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