Block #405,881

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2014, 8:54:35 PM · Difficulty 10.4334 · 6,403,000 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

317c2c5035ff388e53634f3b9c1557976806d76a42a2d86734d1ffc4b30b7efd

View on Chainz ↗

Height

#405,881

Difficulty

10.433371

Transactions

Size

9.83 KB

Version

Bits

0a6ef165

Nonce

13,445,380

Timestamp

2/15/2014, 8:54:35 PM

Confirmations

6,403,000

Mined by

⛏️ P2SHAeytTZcr6YyybHVxEaxdsdMxwzZKbFSWza

Merkle Root

30cce26a26cdf4e6778942a96a70a84e1dc9679b14d38cc4034b05b75d9c9115

Transactions (4)

Coinbasebc2f0d5d780a4c…70c7504ed409c9

1 in → 1 out9.3000 XPM109 B

AeytTZcr…ZKbFSWza

bd180b97c3d09e…23164ad42b42c0

6 in → 2 out19.9104 XPM968 B

AVzyYs4c…cuBcTmiq AeEFDbAk…Qf2gWWpR

b2746fd89426e6…3497627cd7bec7

24 in → 2 out28.6373 XPM3.55 KB

AQZpRbYQ…qesPSdW5 ARb3Ysgh…KHPdCcQQ

2a1f88b1e20cce…c3421500642c91

35 in → 2 out15.0673 XPM5.14 KB

AeZwJAt8…ZVEjFh8b AXbx3pEb…kjumn37r

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.

5.716 × 10⁹⁷(98-digit number)

57166245534130375999…23024014549129420799

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

5.716 × 10⁹⁷(98-digit number)

57166245534130375999…23024014549129420799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.716 × 10⁹⁷(98-digit number)

57166245534130375999…23024014549129420801

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

1.143 × 10⁹⁸(99-digit number)

11433249106826075199…46048029098258841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.143 × 10⁹⁸(99-digit number)

11433249106826075199…46048029098258841601

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

2.286 × 10⁹⁸(99-digit number)

22866498213652150399…92096058196517683199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.286 × 10⁹⁸(99-digit number)

22866498213652150399…92096058196517683201

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

4.573 × 10⁹⁸(99-digit number)

45732996427304300799…84192116393035366399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.573 × 10⁹⁸(99-digit number)

45732996427304300799…84192116393035366401

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

9.146 × 10⁹⁸(99-digit number)

91465992854608601599…68384232786070732799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.146 × 10⁹⁸(99-digit number)

91465992854608601599…68384232786070732801

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 #405,881

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