Block #2,041,283

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2017, 10:21:30 PM · Difficulty 10.6736 · 4,785,433 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ed66ac3389135af01a85881f9bed1ff4b2f914df622ef7ccaefc0d36ae9e41d

View on Chainz ↗

Height

#2,041,283

Difficulty

10.673648

Transactions

Size

5.67 KB

Version

Bits

0aac7439

Nonce

1,916,083,300

Timestamp

3/27/2017, 10:21:30 PM

Confirmations

4,785,433

Mined by

⛏️ P2SHAFnffWjKMNycUWRgT24r87HUkPtwG3o1bt

Merkle Root

a5d2b703ece1ea05845f7d5b3203225efeaee8a1e6b363180092e1f46c1cfd98

Transactions (3)

Coinbase57c347d11c7ced…6b3aaefd740041

1 in → 1 out8.8700 XPM109 B

AFnffWjK…twG3o1bt

011d86babdafa3…931328456597a1

20 in → 2 out3.9382 XPM2.97 KB

AK3PjS76…XHHWngHN AZZNeXWW…PtmY3iEe

2190ce693f9d5e…5d601094077425

17 in → 1 out33.4974 XPM2.50 KB

AP5juu7B…aL8QiDsP

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.

5.773 × 10⁹⁶(97-digit number)

57734905094015515955…63765990589492787199

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

5.773 × 10⁹⁶(97-digit number)

57734905094015515955…63765990589492787199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.773 × 10⁹⁶(97-digit number)

57734905094015515955…63765990589492787201

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

1.154 × 10⁹⁷(98-digit number)

11546981018803103191…27531981178985574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.154 × 10⁹⁷(98-digit number)

11546981018803103191…27531981178985574401

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

2.309 × 10⁹⁷(98-digit number)

23093962037606206382…55063962357971148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.309 × 10⁹⁷(98-digit number)

23093962037606206382…55063962357971148801

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

4.618 × 10⁹⁷(98-digit number)

46187924075212412764…10127924715942297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.618 × 10⁹⁷(98-digit number)

46187924075212412764…10127924715942297601

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

9.237 × 10⁹⁷(98-digit number)

92375848150424825528…20255849431884595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.237 × 10⁹⁷(98-digit number)

92375848150424825528…20255849431884595201

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 #2,041,283

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