Block #408,962

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/18/2014, 1:46:40 AM · Difficulty 10.4240 · 6,397,170 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

021fc1fec4342614f5de4533671d5ec0280035b768753edf4b212ca88ae8f7bc

View on Chainz ↗

Height

#408,962

Difficulty

10.423982

Transactions

Size

1.74 KB

Version

Bits

0a6c8a1d

Nonce

384,725

Timestamp

2/18/2014, 1:46:40 AM

Confirmations

6,397,170

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

572db7c3e4d01f2b31aa1b3a8f26d6c0d24c3d50ee722352cb8a14ef26d8173c

Transactions (5)

Coinbaseaf2b5998ed4fdd…ecf0d34a997206

1 in → 1 out9.3224 XPM116 B

AbwWkWZt…kawDhufa

5b7a56f36d71ae…bf02329fc65e4d

1 in → 2 out42.8628 XPM226 B

APitniQx…P3VJsRWy Abczip68…6Z72j9fo

704cfb9e784c0d…a7ed9863fd15b4

4 in → 1 out12.1800 XPM639 B

ANBKo68j…FknjdrB2

1203a2380f8c21…4c10e65e2ae231

2 in → 1 out2.0800 XPM342 B

AbRLYnep…8mht6KKP

57edcae6652b7e…64c4b10eb541d9

2 in → 2 out3.0381 XPM374 B

ANAuMTQp…5p9EL5ao AeKNrjNj…1NEq95Ta

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.

2.133 × 10⁹¹(92-digit number)

21335483741121751253…66738424052294058899

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

2.133 × 10⁹¹(92-digit number)

21335483741121751253…66738424052294058899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.133 × 10⁹¹(92-digit number)

21335483741121751253…66738424052294058901

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

4.267 × 10⁹¹(92-digit number)

42670967482243502506…33476848104588117799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.267 × 10⁹¹(92-digit number)

42670967482243502506…33476848104588117801

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

8.534 × 10⁹¹(92-digit number)

85341934964487005012…66953696209176235599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.534 × 10⁹¹(92-digit number)

85341934964487005012…66953696209176235601

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

1.706 × 10⁹²(93-digit number)

17068386992897401002…33907392418352471199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.706 × 10⁹²(93-digit number)

17068386992897401002…33907392418352471201

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

3.413 × 10⁹²(93-digit number)

34136773985794802004…67814784836704942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.413 × 10⁹²(93-digit number)

34136773985794802004…67814784836704942401

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