Block #452,345

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 12:37:03 PM · Difficulty 10.3909 · 6,340,087 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1466a81fa8adf8357d10322f70b18384f89be525bf35537a1ed6028013c59688

View on Chainz ↗

Height

#452,345

Difficulty

10.390874

Transactions

Size

427 B

Version

Bits

0a641057

Nonce

266,679

Timestamp

3/20/2014, 12:37:03 PM

Confirmations

6,340,087

Merkle Root

bce5d9405ad1f03e7decb16552a76e81588d8a45a28cec9c091e23a3a384aae4

Transactions (2)

Coinbase13472ed0c5c73e…fa02d8cb356a63

1 in → 1 out9.2600 XPM109 B

AbTrJYvk…GouFQ3Wr

27df59a70cb682…c60fbd5c375d42

1 in → 2 out10.0100 XPM226 B

AHcM27Ef…mJ1RzpPY ALsgHeEX…P4fAroNJ

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.

5.725 × 10⁹⁸(99-digit number)

57252088812212921865…23813565356559470919

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

5.725 × 10⁹⁸(99-digit number)

57252088812212921865…23813565356559470919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.725 × 10⁹⁸(99-digit number)

57252088812212921865…23813565356559470921

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

1.145 × 10⁹⁹(100-digit number)

11450417762442584373…47627130713118941839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.145 × 10⁹⁹(100-digit number)

11450417762442584373…47627130713118941841

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

2.290 × 10⁹⁹(100-digit number)

22900835524885168746…95254261426237883679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.290 × 10⁹⁹(100-digit number)

22900835524885168746…95254261426237883681

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

4.580 × 10⁹⁹(100-digit number)

45801671049770337492…90508522852475767359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.580 × 10⁹⁹(100-digit number)

45801671049770337492…90508522852475767361

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

9.160 × 10⁹⁹(100-digit number)

91603342099540674985…81017045704951534719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.160 × 10⁹⁹(100-digit number)

91603342099540674985…81017045704951534721

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