Block #451,747

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 4:15:42 AM · Difficulty 10.3790 · 6,375,264 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26853a604af03cbe19a59e6e26ad24b7d16b4d76b32b6a4ce37486e7b8ebcde0

View on Chainz ↗

Height

#451,747

Difficulty

10.379035

Transactions

Size

1.30 KB

Version

Bits

0a610877

Nonce

178,114

Timestamp

3/20/2014, 4:15:42 AM

Confirmations

6,375,264

Mined by

⛏️ mAHQyfiZn7AWhbhzXeEptuwLriCsQbeqE98

Merkle Root

8e46b81c7b70ca4e4912e1c135f1b03b8c79797119a6f7f3d2d878da477bc0cb

Transactions (3)

Coinbasec19c55ffa52853…abb2c74fede807

1 in → 7 out9.2900 XPM301 B

AHQyfiZn…sQbeqE98 ANKzHTAZ…nyUjaxVT AWCjgrw2…MnFAU7HX AXDyRw5b…CSGugJcJ ARJu9Qoh…JpP9irBQ

934c68c3f10aa4…47e2f4c5cf1deb

5 in → 2 out28.0408 XPM716 B

AdkoPBg8…wE31p5Zg Abo5nRbx…qf7mMxAq

b032e03f94ea8c…88351e1448ad39

1 in → 2 out1163.8900 XPM226 B

AJjnK9uC…VreFquR4 AXDM369a…NGp81Zam

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.

4.065 × 10⁹⁷(98-digit number)

40651237459575423931…08706667350339566719

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

4.065 × 10⁹⁷(98-digit number)

40651237459575423931…08706667350339566719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.065 × 10⁹⁷(98-digit number)

40651237459575423931…08706667350339566721

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

8.130 × 10⁹⁷(98-digit number)

81302474919150847862…17413334700679133439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.130 × 10⁹⁷(98-digit number)

81302474919150847862…17413334700679133441

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

1.626 × 10⁹⁸(99-digit number)

16260494983830169572…34826669401358266879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.626 × 10⁹⁸(99-digit number)

16260494983830169572…34826669401358266881

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

3.252 × 10⁹⁸(99-digit number)

32520989967660339144…69653338802716533759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.252 × 10⁹⁸(99-digit number)

32520989967660339144…69653338802716533761

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

6.504 × 10⁹⁸(99-digit number)

65041979935320678289…39306677605433067519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.504 × 10⁹⁸(99-digit number)

65041979935320678289…39306677605433067521

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 #451,747

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