Block #452,729

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/20/2014, 6:55:25 PM · Difficulty 10.3914 · 6,357,031 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ebf06d4b5f3f2ed84e5a0d769ef2b41f855c18cf81a0d47c945190573ff77e90

View on Chainz ↗

Height

#452,729

Difficulty

10.391432

Transactions

Size

2.27 KB

Version

Bits

0a6434e5

Nonce

7,507

Timestamp

3/20/2014, 6:55:25 PM

Confirmations

6,357,031

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

24129c9df3f7003a3981b7887a60f4275574cd4126b282bbc8097acb7415b535

Transactions (2)

Coinbaseba96b9a5b3afe2…5db01584920052

1 in → 1 out9.2800 XPM116 B

AbwWkWZt…kawDhufa

60ffb919b32bb4…6a48db573d2c94

8 in → 27 out67.7073 XPM2.07 KB

AUkdqaxr…4jcbMUQ7 AR8WV4KS…SChNuf3B APY7DzaT…vd2C7Uf6 ALnQa3dm…bib1k4d3 AV8poZoT…i3Ac3wP1

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.

1.029 × 10⁹⁷(98-digit number)

10293048707269768000…60508515686137891499

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

1.029 × 10⁹⁷(98-digit number)

10293048707269768000…60508515686137891499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.029 × 10⁹⁷(98-digit number)

10293048707269768000…60508515686137891501

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

2.058 × 10⁹⁷(98-digit number)

20586097414539536000…21017031372275782999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.058 × 10⁹⁷(98-digit number)

20586097414539536000…21017031372275783001

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

4.117 × 10⁹⁷(98-digit number)

41172194829079072000…42034062744551565999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.117 × 10⁹⁷(98-digit number)

41172194829079072000…42034062744551566001

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

8.234 × 10⁹⁷(98-digit number)

82344389658158144001…84068125489103131999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.234 × 10⁹⁷(98-digit number)

82344389658158144001…84068125489103132001

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

1.646 × 10⁹⁸(99-digit number)

16468877931631628800…68136250978206263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.646 × 10⁹⁸(99-digit number)

16468877931631628800…68136250978206264001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.293 × 10⁹⁸(99-digit number)

32937755863263257600…36272501956412527999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #452,729

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