Block #1,083,602

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/31/2015, 12:44:41 AM · Difficulty 10.7703 · 5,733,602 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07a9e1e661766e85075bc3391b769a9c0d4623f2f088595d7d03fdefa39aec23

View on Chainz ↗

Height

#1,083,602

Difficulty

10.770268

Transactions

Size

1.51 KB

Version

Bits

0ac53049

Nonce

76,972,206

Timestamp

5/31/2015, 12:44:41 AM

Confirmations

5,733,602

Mined by

⛏️ P2SHAPMmHJSgbQ6Bt391J2P4dW2MLVVvxU2s8e

Merkle Root

223cfa799850c73a5675f68343bb2daf25fd486cbd657cc72d3a4e5c7445f0cd

Transactions (5)

Coinbasec7cc6f81e03815…82494401d9087f

1 in → 1 out8.6500 XPM110 B

APMmHJSg…VvxU2s8e

1600261d04d231…0cb6032d727927

1 in → 2 out8.6000 XPM225 B

ATeq89Xp…TmcKZiDY AVZwze3C…1DNKwKx6

ed5f1c025d2fd4…0571d764c3ae9a

1 in → 2 out8.6000 XPM227 B

AXrTw46X…e1dGvSFf ANyXS4ZW…59re6WyF

841ea0614edf15…5659debd167b13

4 in → 2 out5.0241 XPM671 B

ANia7wgK…VR264iFL AHyqbSeY…DnjUiDto

1169418304bb31…6c63ffcfd3afc9

1 in → 2 out3.2869 XPM226 B

Ac8Z8gqy…UoiSucvL Ae7YXEyn…hnSYZsCr

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.

3.113 × 10⁹⁶(97-digit number)

31136167379747405747…60791223977020825599

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

3.113 × 10⁹⁶(97-digit number)

31136167379747405747…60791223977020825599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.113 × 10⁹⁶(97-digit number)

31136167379747405747…60791223977020825601

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

6.227 × 10⁹⁶(97-digit number)

62272334759494811495…21582447954041651199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.227 × 10⁹⁶(97-digit number)

62272334759494811495…21582447954041651201

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

1.245 × 10⁹⁷(98-digit number)

12454466951898962299…43164895908083302399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.245 × 10⁹⁷(98-digit number)

12454466951898962299…43164895908083302401

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

2.490 × 10⁹⁷(98-digit number)

24908933903797924598…86329791816166604799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.490 × 10⁹⁷(98-digit number)

24908933903797924598…86329791816166604801

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

4.981 × 10⁹⁷(98-digit number)

49817867807595849196…72659583632333209599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.981 × 10⁹⁷(98-digit number)

49817867807595849196…72659583632333209601

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 #1,083,602

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