Block #397,389

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 1:46:58 AM · Difficulty 10.4130 · 6,412,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

05d6b4b7ecd47be6066673fc8747450a2887cd0e50b9b2d6a405808c22b72183

View on Chainz ↗

Height

#397,389

Difficulty

10.413013

Transactions

Size

2.66 KB

Version

Bits

0a69bb31

Nonce

306,966

Timestamp

2/10/2014, 1:46:58 AM

Confirmations

6,412,832

Mined by

⛏️ MaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1566ad87db5c0649fe8d70a5668a7ff9d157e1be62c20d59ae570e16618f5050

Transactions (4)

Coinbase9b7f2eeaaf2b9c…4d17c2e4cfb7ac

1 in → 26 out9.2100 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AGQxR1oS…2N1xAZXN

f8c8c6802bbc97…affead3e8e5a26

6 in → 16 out55.2300 XPM1.21 KB

ASazS3Sd…EfFBiQBS AHbu8w6V…13P7BwSQ AZSVhd9Y…rYTSwNV1 AbdybaRr…aB9c2nMP AVrD6maY…W77cdqzz

c399c84e6565ca…aa7c31b8bd4ef5

1 in → 2 out7.1371 XPM226 B

AKbt8qNV…cgrRJA2t ASPtsETp…M4NdngCg

4e8e34ac45b947…6831804702515f

1 in → 2 out6.1051 XPM225 B

AYs3QkuJ…UDVrEWbb ATneuL4c…r6oZjB9J

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.

1.933 × 10⁹²(93-digit number)

19337678922963236231…99617208689353715039

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

1.933 × 10⁹²(93-digit number)

19337678922963236231…99617208689353715039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.933 × 10⁹²(93-digit number)

19337678922963236231…99617208689353715041

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

3.867 × 10⁹²(93-digit number)

38675357845926472463…99234417378707430079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.867 × 10⁹²(93-digit number)

38675357845926472463…99234417378707430081

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

7.735 × 10⁹²(93-digit number)

77350715691852944926…98468834757414860159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.735 × 10⁹²(93-digit number)

77350715691852944926…98468834757414860161

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

1.547 × 10⁹³(94-digit number)

15470143138370588985…96937669514829720319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.547 × 10⁹³(94-digit number)

15470143138370588985…96937669514829720321

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

3.094 × 10⁹³(94-digit number)

30940286276741177970…93875339029659440639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.094 × 10⁹³(94-digit number)

30940286276741177970…93875339029659440641

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 #397,389

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