Block #252,384

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 1:15:14 PM · Difficulty 9.9711 · 6,557,176 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

72c7c34ceae15dc25cb5c0d6d1e76be8e127848997c936156890b87639e6411c

View on Chainz ↗

Height

#252,384

Difficulty

9.971088

Transactions

Size

5.41 KB

Version

Bits

09f89931

Nonce

176,639

Timestamp

11/9/2013, 1:15:14 PM

Confirmations

6,557,176

Mined by

⛏️ P2SHAeQot7NswFySABLT93i3UWiwHzUjK8d5xs

Merkle Root

d09cfcb919b631eba3af4436b8b4cafc4bce27f7e5cab1bdb973941d26864ec4

Transactions (3)

Coinbase7842b02046383e…a0f87d5d0d527b

1 in → 1 out10.1000 XPM109 B

AeQot7Ns…UjK8d5xs

753b9736b74b9e…be405c8a5d5777

3 in → 2 out407.5577 XPM522 B

AGdiXVj2…YQJcbe3G Ab97PuhA…JV9avpHm

8934d8dd292ee9…fd20150400dc7c

32 in → 2 out317.8325 XPM4.70 KB

AaeB7g5p…gowrDK46 AHjSuiYP…mkASp3eH

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.

4.399 × 10⁹³(94-digit number)

43994956150996251987…32620551684341841919

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

4.399 × 10⁹³(94-digit number)

43994956150996251987…32620551684341841919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.399 × 10⁹³(94-digit number)

43994956150996251987…32620551684341841921

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

8.798 × 10⁹³(94-digit number)

87989912301992503974…65241103368683683839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.798 × 10⁹³(94-digit number)

87989912301992503974…65241103368683683841

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

1.759 × 10⁹⁴(95-digit number)

17597982460398500794…30482206737367367679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.759 × 10⁹⁴(95-digit number)

17597982460398500794…30482206737367367681

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

3.519 × 10⁹⁴(95-digit number)

35195964920797001589…60964413474734735359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.519 × 10⁹⁴(95-digit number)

35195964920797001589…60964413474734735361

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

7.039 × 10⁹⁴(95-digit number)

70391929841594003179…21928826949469470719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.039 × 10⁹⁴(95-digit number)

70391929841594003179…21928826949469470721

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 #252,384

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