Block #410,383

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2014, 1:08:18 AM · Difficulty 10.4275 · 6,399,838 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c464e10a84305610a829b9546a542085e250c4bc6cba4c4e3c043bf1bf143fe2

View on Chainz ↗

Height

#410,383

Difficulty

10.427495

Transactions

Size

2.04 KB

Version

Bits

0a6d7058

Nonce

72,135

Timestamp

2/19/2014, 1:08:18 AM

Confirmations

6,399,838

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4d41e7faf2fa3422c4023cb924e3d3dfa22a4fcec07bc136bfed5451559b8f4e

Transactions (2)

Coinbaseedb678522740e2…495d34641e5c24

1 in → 1 out9.2000 XPM110 B

AeKNrjNj…1NEq95Ta

0ad03d83e25927…3db39f707c1f5b

9 in → 25 out82.6200 XPM1.84 KB

AbtSx63H…NujNdz31 AS7tPNSw…YtYeFveL AeKNrjNj…1NEq95Ta AZQMW3t7…qdVF2oyY AJQWwVXB…L2b71Qbt

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.

2.291 × 10⁹³(94-digit number)

22913173513248833409…64375844464820682049

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

2.291 × 10⁹³(94-digit number)

22913173513248833409…64375844464820682049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.291 × 10⁹³(94-digit number)

22913173513248833409…64375844464820682051

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

4.582 × 10⁹³(94-digit number)

45826347026497666818…28751688929641364099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.582 × 10⁹³(94-digit number)

45826347026497666818…28751688929641364101

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

9.165 × 10⁹³(94-digit number)

91652694052995333637…57503377859282728199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.165 × 10⁹³(94-digit number)

91652694052995333637…57503377859282728201

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

1.833 × 10⁹⁴(95-digit number)

18330538810599066727…15006755718565456399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.833 × 10⁹⁴(95-digit number)

18330538810599066727…15006755718565456401

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

3.666 × 10⁹⁴(95-digit number)

36661077621198133455…30013511437130912799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.666 × 10⁹⁴(95-digit number)

36661077621198133455…30013511437130912801

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 #410,383

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