Block #297,736

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/6/2013, 7:12:37 PM · Difficulty 9.9920 · 6,512,571 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88f0ad125b0e55166d5d274dcee9ce571cdbdf52d6b26028499b89b541214474

View on Chainz ↗

Height

#297,736

Difficulty

9.992035

Transactions

Size

1.81 KB

Version

Bits

09fdf600

Nonce

8,035

Timestamp

12/6/2013, 7:12:37 PM

Confirmations

6,512,571

Mined by

⛏️ aR!ARzXge7STrHg8ZTMRW57MCNAWRCEjL5oYm

Merkle Root

76f3d8c6dece7a04a1d857f05fb0a724167383ee04bd09ba8bf432fb9c5e041d

Transactions (4)

Coinbased64a91dd4b4082…7ea7cce1c98511

1 in → 30 out9.9800 XPM1.06 KB

ARzXge7S…CEjL5oYm AYtDvcGs…VuAcA7m7 AHuJ9wYh…BGmgHrKZ AQwRN8bE…V8PsTcY9 Ad9pSzHt…cpJ3y2zz

044cd50ab1a01f…4c230920ca7578

1 in → 2 out9.9900 XPM225 B

AWUdBJHf…tkXrExRG AJbyAqDJ…gsAaWxdb

b8a534dbcec7fa…bf5dd985ce3121

1 in → 2 out9.9900 XPM226 B

ANgU6Lbw…woi6UGQx AWvfDWEh…JutFJH2N

63c78b51023823…c5b0d046275c96

1 in → 2 out9.9900 XPM226 B

ASVe5T17…nR6zr1YX AQRsFW4v…ZyH1MGt9

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.

3.090 × 10⁹⁸(99-digit number)

30902840917493040013…47382860413263170559

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

3.090 × 10⁹⁸(99-digit number)

30902840917493040013…47382860413263170559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.090 × 10⁹⁸(99-digit number)

30902840917493040013…47382860413263170561

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

6.180 × 10⁹⁸(99-digit number)

61805681834986080027…94765720826526341119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.180 × 10⁹⁸(99-digit number)

61805681834986080027…94765720826526341121

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

1.236 × 10⁹⁹(100-digit number)

12361136366997216005…89531441653052682239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.236 × 10⁹⁹(100-digit number)

12361136366997216005…89531441653052682241

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

2.472 × 10⁹⁹(100-digit number)

24722272733994432011…79062883306105364479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.472 × 10⁹⁹(100-digit number)

24722272733994432011…79062883306105364481

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

4.944 × 10⁹⁹(100-digit number)

49444545467988864022…58125766612210728959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.944 × 10⁹⁹(100-digit number)

49444545467988864022…58125766612210728961

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 #297,736

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