Block #283,436

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 5:49:37 PM · Difficulty 9.9811 · 6,526,512 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

44658e0a6b8bf7575867dff23fa4e1717467b3bb601f2e84d76175ed6294e7ab

View on Chainz ↗

Height

#283,436

Difficulty

9.981116

Transactions

Size

4.47 KB

Version

Bits

09fb2a6a

Nonce

13,614

Timestamp

11/29/2013, 5:49:37 PM

Confirmations

6,526,512

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a9b5e5de59c59b202344b3aaaab15b392d2847ff74d5850c7c406d3458bfe31a

Transactions (4)

Coinbase576f77cc4f19cf…8a8179778b0a48

1 in → 1 out10.0800 XPM110 B

AeKNrjNj…1NEq95Ta

9d5728268cdfea…81a159ffab089a

24 in → 2 out8.7753 XPM3.54 KB

AKzfbkVj…ENAzhZfz AckH9P8M…G59KoSeH

0af9894a7bed39…e03a622861d9f4

1 in → 2 out4.6472 XPM226 B

Ab3dSvM7…Qoxxb9tp AMJSAL6E…Z117At5c

7b9e34037aed1c…d1db90aebdbbf1

3 in → 2 out1.0624 XPM521 B

AP9AEwjy…2CyYAeLQ AMtBbjYe…ZJtv85ud

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.

1.191 × 10⁹⁸(99-digit number)

11919274576040635431…10921776229186898489

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

1.191 × 10⁹⁸(99-digit number)

11919274576040635431…10921776229186898489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.191 × 10⁹⁸(99-digit number)

11919274576040635431…10921776229186898491

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

2.383 × 10⁹⁸(99-digit number)

23838549152081270862…21843552458373796979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.383 × 10⁹⁸(99-digit number)

23838549152081270862…21843552458373796981

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

4.767 × 10⁹⁸(99-digit number)

47677098304162541724…43687104916747593959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.767 × 10⁹⁸(99-digit number)

47677098304162541724…43687104916747593961

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

9.535 × 10⁹⁸(99-digit number)

95354196608325083448…87374209833495187919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.535 × 10⁹⁸(99-digit number)

95354196608325083448…87374209833495187921

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

1.907 × 10⁹⁹(100-digit number)

19070839321665016689…74748419666990375839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.907 × 10⁹⁹(100-digit number)

19070839321665016689…74748419666990375841

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 #283,436

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