Block #399,034

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 4:27:20 AM · Difficulty 10.4192 · 6,427,614 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

934bd7db6e2606a5ec7c251ef4534d918b6062f6ea042ebdd96920b2c964621e

View on Chainz ↗

Height

#399,034

Difficulty

10.419183

Transactions

Size

2.00 KB

Version

Bits

0a6b4f98

Nonce

186,910

Timestamp

2/11/2014, 4:27:20 AM

Confirmations

6,427,614

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9e3c61c027e6a6386e4fcf23f0c2ad7d94a07e3e0a7d7b5654e29e108173a6bc

Transactions (2)

Coinbasebea686cd61af8a…a5c142acc66382

1 in → 1 out9.2200 XPM110 B

AeKNrjNj…1NEq95Ta

c7377cc116d65c…593bc539b0b8eb

11 in → 8 out23.3034 XPM1.80 KB

AZVFkon3…USAZdbmu AKJx7ewq…cdjZ12Jp AeKNrjNj…1NEq95Ta AMMSpxFF…5AwmfBJ2 AHCuz9P2…41tUcRdy

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.

4.944 × 10⁹⁸(99-digit number)

49445622839460198641…05606536195993317119

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

4.944 × 10⁹⁸(99-digit number)

49445622839460198641…05606536195993317119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.944 × 10⁹⁸(99-digit number)

49445622839460198641…05606536195993317121

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

9.889 × 10⁹⁸(99-digit number)

98891245678920397282…11213072391986634239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.889 × 10⁹⁸(99-digit number)

98891245678920397282…11213072391986634241

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

1.977 × 10⁹⁹(100-digit number)

19778249135784079456…22426144783973268479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.977 × 10⁹⁹(100-digit number)

19778249135784079456…22426144783973268481

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

3.955 × 10⁹⁹(100-digit number)

39556498271568158912…44852289567946536959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.955 × 10⁹⁹(100-digit number)

39556498271568158912…44852289567946536961

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

7.911 × 10⁹⁹(100-digit number)

79112996543136317825…89704579135893073919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.911 × 10⁹⁹(100-digit number)

79112996543136317825…89704579135893073921

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 #399,034

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