Block #407,943

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 7:57:07 AM · Difficulty 10.4294 · 6,391,261 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

79d1c815673c3d9499138a28803ce6e7d9cd30646a91825c6239c219d6b9df8f

View on Chainz ↗

Height

#407,943

Difficulty

10.429386

Transactions

Size

26.97 KB

Version

Bits

0a6dec3a

Nonce

335,856

Timestamp

2/17/2014, 7:57:07 AM

Confirmations

6,391,261

Mined by

⛏️ 9XAMW1p9oTkBzM1hi3okaKfJzfWi2TzdaZxH

Merkle Root

d169bc6a214f2bfd8f245d778541ee362dfd2e30a61399175a4d51913ea89810

Transactions (4)

Coinbasec7dc33b56a9394…eb28c07758c8d4

1 in → 23 out9.4700 XPM845 B

AMW1p9oT…2TzdaZxH AZr7Ptuw…CM4Yw5jq AcgDwGo8…BBFwbjVo AUzEPJFG…kYkA5U9V AczyTBWn…bEQQj33u

b24646e948e75b…781aabbab1b666

3 in → 7 out18.7529 XPM622 B

ATZMyfv3…4iQr9XYS AeKNrjNj…1NEq95Ta AZBgp11g…CPJiApFR ANAuMTQp…5p9EL5ao AUDA3a2M…mDChw1vJ

de9a3dbec00cc5…f5a4c2ec87e00d

5 in → 2 out9.6552 XPM820 B

AcJnYoGF…TGnPwKig AbjJtYv5…kQDvMZe1

00283895555ab4…bca44da6649297

170 in → 2 out71.1111 XPM24.65 KB

AKyYb3pY…3fvUcwxK ARKdWCwe…nCLJDuK6

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.

4.909 × 10⁹⁵(96-digit number)

49092327462252688259…82182850110971952299

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

4.909 × 10⁹⁵(96-digit number)

49092327462252688259…82182850110971952299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.909 × 10⁹⁵(96-digit number)

49092327462252688259…82182850110971952301

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

9.818 × 10⁹⁵(96-digit number)

98184654924505376518…64365700221943904599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.818 × 10⁹⁵(96-digit number)

98184654924505376518…64365700221943904601

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

1.963 × 10⁹⁶(97-digit number)

19636930984901075303…28731400443887809199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.963 × 10⁹⁶(97-digit number)

19636930984901075303…28731400443887809201

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

3.927 × 10⁹⁶(97-digit number)

39273861969802150607…57462800887775618399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.927 × 10⁹⁶(97-digit number)

39273861969802150607…57462800887775618401

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

7.854 × 10⁹⁶(97-digit number)

78547723939604301214…14925601775551236799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.854 × 10⁹⁶(97-digit number)

78547723939604301214…14925601775551236801

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