Block #395,780

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2014, 11:29:48 PM · Difficulty 10.4098 · 6,395,707 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

994d2902cf8b903c3fcc6dda2499b766597368230637da036b34bf69b9583f0b

View on Chainz ↗

Height

#395,780

Difficulty

10.409821

Transactions

Size

1.51 KB

Version

Bits

0a68ea07

Nonce

110,114

Timestamp

2/8/2014, 11:29:48 PM

Confirmations

6,395,707

Merkle Root

ca15ba40d3426787cbecb8b04cf6394ecac87ea76b779fdcbccc87b57fa7dd4c

Transactions (5)

Coinbasead849f374d4b81…097509ca009c83

1 in → 1 out9.2500 XPM110 B

AeKNrjNj…1NEq95Ta

c51c142caeef50…d6bd23c769b1d3

2 in → 2 out11.3074 XPM374 B

AJJu16ii…1zZTWnqc ALTGALf9…fEZZmxSk

7eda444652fc5b…dbbde0ef71773c

1 in → 2 out8.1393 XPM226 B

AeZZPYHj…5K1XcjZJ APdHU8K7…fbwZZD86

8d0c7cf5dcdbfd…3c04d64ceb2868

1 in → 2 out8.1392 XPM225 B

ARZXZzCt…NYs31Mo5 AXXJXZV6…sBSaZA5o

e2d2033cf4a075…b1d58eacbeff50

3 in → 2 out5.5110 XPM522 B

ASCN5kqi…Q4SzwDb5 AWhqCNs1…mTz9bU71

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.

9.533 × 10⁹⁶(97-digit number)

95331186586523836680…55476797117121136359

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

9.533 × 10⁹⁶(97-digit number)

95331186586523836680…55476797117121136359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.533 × 10⁹⁶(97-digit number)

95331186586523836680…55476797117121136361

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

1.906 × 10⁹⁷(98-digit number)

19066237317304767336…10953594234242272719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.906 × 10⁹⁷(98-digit number)

19066237317304767336…10953594234242272721

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

3.813 × 10⁹⁷(98-digit number)

38132474634609534672…21907188468484545439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.813 × 10⁹⁷(98-digit number)

38132474634609534672…21907188468484545441

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

7.626 × 10⁹⁷(98-digit number)

76264949269219069344…43814376936969090879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.626 × 10⁹⁷(98-digit number)

76264949269219069344…43814376936969090881

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

1.525 × 10⁹⁸(99-digit number)

15252989853843813868…87628753873938181759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.525 × 10⁹⁸(99-digit number)

15252989853843813868…87628753873938181761

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