Block #393,816

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/7/2014, 10:34:17 AM · Difficulty 10.4368 · 6,405,539 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b86136e9460a9ff70e049287d978027718881a44c5909b6e4775b54b9e5822b

View on Chainz ↗

Height

#393,816

Difficulty

10.436844

Transactions

Size

1.52 KB

Version

Bits

0a6fd502

Nonce

99,982

Timestamp

2/7/2014, 10:34:17 AM

Confirmations

6,405,539

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

505f17992e446f685ee78988d57cc89309532e7268aec47b508fd7e3fc61e6ab

Transactions (5)

Coinbasef4d56f36c37e6b…6985fb170ea479

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

f75f89fac0446b…52f1c9719c6be7

1 in → 2 out7.0806 XPM227 B

AXoTQRew…B4KkctQh AJtKhSB8…jbGJEzbR

8ec6eb6b0c49cd…c44008080131e0

1 in → 2 out2.9381 XPM225 B

ASXDGAbm…nifJSMT4 AJjsX4t4…gtmJp9SX

062a684f7ad927…ccf9058b4e0963

1 in → 2 out5.5851 XPM226 B

Ae9MjotM…GYBmNQuM AYVyegUo…88drMYWV

b2e7b8ba9f41aa…0756ff326317d3

4 in → 2 out5.0153 XPM669 B

AVcHdq3H…GA7Y919T AQtYU8QD…BXSN7tbr

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.

2.746 × 10⁹⁷(98-digit number)

27462603775258678959…74997096632932069659

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

2.746 × 10⁹⁷(98-digit number)

27462603775258678959…74997096632932069659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.746 × 10⁹⁷(98-digit number)

27462603775258678959…74997096632932069661

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

5.492 × 10⁹⁷(98-digit number)

54925207550517357919…49994193265864139319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.492 × 10⁹⁷(98-digit number)

54925207550517357919…49994193265864139321

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

1.098 × 10⁹⁸(99-digit number)

10985041510103471583…99988386531728278639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.098 × 10⁹⁸(99-digit number)

10985041510103471583…99988386531728278641

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

2.197 × 10⁹⁸(99-digit number)

21970083020206943167…99976773063456557279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.197 × 10⁹⁸(99-digit number)

21970083020206943167…99976773063456557281

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

4.394 × 10⁹⁸(99-digit number)

43940166040413886335…99953546126913114559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.394 × 10⁹⁸(99-digit number)

43940166040413886335…99953546126913114561

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