Block #400,964

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/12/2014, 10:59:48 AM · Difficulty 10.4304 · 6,391,630 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

374df95b063220a6927acfcf69005ed40aa09cef0e8e8d8bfdaef6dcf611d205

View on Chainz ↗

Height

#400,964

Difficulty

10.430419

Transactions

Size

808 B

Version

Bits

0a6e2fea

Nonce

78,152

Timestamp

2/12/2014, 10:59:48 AM

Confirmations

6,391,630

Merkle Root

99c13cc95ccb791f751888ec5871c13e267a4dd281f9c8eaf14cdadb4a4f0290

Transactions (3)

Coinbase4e681b138e919a…1a4d8a32e1c37c

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

c2b763a372fdb0…4c0a67a62aae1a

2 in → 2 out11.3539 XPM375 B

AVyQNyFx…DgDVk7nS ATZUp49D…xaoNMsmK

8854b599a13cf6…7117a21ef04500

1 in → 2 out4.1245 XPM225 B

AV9xh7Hb…GpwqvLUR ANo6FWiG…DLDCMjro

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.

1.936 × 10⁹⁹(100-digit number)

19368944075372374415…27408887724965927679

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

1.936 × 10⁹⁹(100-digit number)

19368944075372374415…27408887724965927679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.936 × 10⁹⁹(100-digit number)

19368944075372374415…27408887724965927681

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

3.873 × 10⁹⁹(100-digit number)

38737888150744748831…54817775449931855359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.873 × 10⁹⁹(100-digit number)

38737888150744748831…54817775449931855361

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

7.747 × 10⁹⁹(100-digit number)

77475776301489497662…09635550899863710719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.747 × 10⁹⁹(100-digit number)

77475776301489497662…09635550899863710721

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

1.549 × 10¹⁰⁰(101-digit number)

15495155260297899532…19271101799727421439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.549 × 10¹⁰⁰(101-digit number)

15495155260297899532…19271101799727421441

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

3.099 × 10¹⁰⁰(101-digit number)

30990310520595799064…38542203599454842879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.099 × 10¹⁰⁰(101-digit number)

30990310520595799064…38542203599454842881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.198 × 10¹⁰⁰(101-digit number)

61980621041191598129…77084407198909685759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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