Block #401,240

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/12/2014, 3:12:25 PM · Difficulty 10.4337 · 6,404,917 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe2fa15e9e94d8f2c7f45411926562736cf4df019070e418c9878eb63ae0cb2f

View on Chainz ↗

Height

#401,240

Difficulty

10.433651

Transactions

Size

902 B

Version

Bits

0a6f03c1

Nonce

10,886

Timestamp

2/12/2014, 3:12:25 PM

Confirmations

6,404,917

Mined by

⛏️ XaRwuAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

de16d63c8346f5ea3004b08e9296d5ada8213a12a15f55caff284069380a7fcf

Transactions (1)

Coinbasede16d63c8346f5…284069380a7fcf

1 in → 22 out9.1700 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6 AN8nUzff…YcDfRDQ2

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.

4.510 × 10⁹⁶(97-digit number)

45106689114273930333…41343561861281430339

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

4.510 × 10⁹⁶(97-digit number)

45106689114273930333…41343561861281430339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.510 × 10⁹⁶(97-digit number)

45106689114273930333…41343561861281430341

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

9.021 × 10⁹⁶(97-digit number)

90213378228547860667…82687123722562860679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.021 × 10⁹⁶(97-digit number)

90213378228547860667…82687123722562860681

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

1.804 × 10⁹⁷(98-digit number)

18042675645709572133…65374247445125721359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.804 × 10⁹⁷(98-digit number)

18042675645709572133…65374247445125721361

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

3.608 × 10⁹⁷(98-digit number)

36085351291419144267…30748494890251442719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.608 × 10⁹⁷(98-digit number)

36085351291419144267…30748494890251442721

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

7.217 × 10⁹⁷(98-digit number)

72170702582838288534…61496989780502885439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.217 × 10⁹⁷(98-digit number)

72170702582838288534…61496989780502885441

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