Block #406,485

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/16/2014, 7:20:05 AM · Difficulty 10.4313 · 6,411,460 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ba38dd9b0edb7cf7b7fe42ac85bc7e542019acb8be2eece62135c5add539cb49

View on Chainz ↗

Height

#406,485

Difficulty

10.431268

Transactions

Size

887 B

Version

Bits

0a6e6797

Nonce

140,321

Timestamp

2/16/2014, 7:20:05 AM

Confirmations

6,411,460

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c199780155add3357b12eae3a41697fcaf61708ad8df321ad57a6ada4c038cd8

Transactions (3)

Coinbase7bcf760bec6dc5…a08929a13c57bc

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

b6008306fc6a10…613bea4b084cfe

3 in → 1 out3.7838 XPM488 B

AdGtcVUn…RLRGbs5n

788c6873f780c3…9504e45a0e4178

1 in → 1 out3.0242 XPM192 B

Af1415qo…scuPteQ8

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.

1.099 × 10⁹⁸(99-digit number)

10997078187705277665…18112843508387766239

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

1.099 × 10⁹⁸(99-digit number)

10997078187705277665…18112843508387766239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.099 × 10⁹⁸(99-digit number)

10997078187705277665…18112843508387766241

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

2.199 × 10⁹⁸(99-digit number)

21994156375410555331…36225687016775532479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.199 × 10⁹⁸(99-digit number)

21994156375410555331…36225687016775532481

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

4.398 × 10⁹⁸(99-digit number)

43988312750821110663…72451374033551064959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.398 × 10⁹⁸(99-digit number)

43988312750821110663…72451374033551064961

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

8.797 × 10⁹⁸(99-digit number)

87976625501642221327…44902748067102129919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.797 × 10⁹⁸(99-digit number)

87976625501642221327…44902748067102129921

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

1.759 × 10⁹⁹(100-digit number)

17595325100328444265…89805496134204259839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.759 × 10⁹⁹(100-digit number)

17595325100328444265…89805496134204259841

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 #406,485

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