Block #398,197

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 2:00:05 PM · Difficulty 10.4220 · 6,405,246 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de388eb9f1db1d4179508ff33e22ec205fe58db6b5de1cbcd5a154c16b07678a

View on Chainz ↗

Height

#398,197

Difficulty

10.421974

Transactions

Size

1.07 KB

Version

Bits

0a6c067e

Nonce

111,863

Timestamp

2/10/2014, 2:00:05 PM

Confirmations

6,405,246

Mined by

⛏️ uaR#AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d0828d094938fe97ce3e29be98e6f7852a92b9a09e03eb1bd430b8d71e07490c

Transactions (2)

Coinbasec019b29fdfb770…e1b3120537c340

1 in → 22 out9.1900 XPM811 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 ALqxX1WA…hsKjbnXn

edfc646ace3db7…5a55c8370bc8b6

1 in → 1 out6.8200 XPM191 B

Aa71CFCG…iAdKaZo5

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.

2.588 × 10⁹⁸(99-digit number)

25885615103875405469…58657337377349299859

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

2.588 × 10⁹⁸(99-digit number)

25885615103875405469…58657337377349299859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.588 × 10⁹⁸(99-digit number)

25885615103875405469…58657337377349299861

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

5.177 × 10⁹⁸(99-digit number)

51771230207750810939…17314674754698599719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.177 × 10⁹⁸(99-digit number)

51771230207750810939…17314674754698599721

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

1.035 × 10⁹⁹(100-digit number)

10354246041550162187…34629349509397199439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.035 × 10⁹⁹(100-digit number)

10354246041550162187…34629349509397199441

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

2.070 × 10⁹⁹(100-digit number)

20708492083100324375…69258699018794398879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.070 × 10⁹⁹(100-digit number)

20708492083100324375…69258699018794398881

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

4.141 × 10⁹⁹(100-digit number)

41416984166200648751…38517398037588797759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.141 × 10⁹⁹(100-digit number)

41416984166200648751…38517398037588797761

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