Block #334,565

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2013, 2:25:23 PM · Difficulty 10.1576 · 6,479,517 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

10c9c8b22ddc84dfabdcd020a88857057cd3fbf521496f1333301b411787ece0

View on Chainz ↗

Height

#334,565

Difficulty

10.157563

Transactions

Size

1.22 KB

Version

Bits

0a285610

Nonce

13,263

Timestamp

12/29/2013, 2:25:23 PM

Confirmations

6,479,517

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

cfd40df776bfdfc44f5b40e8ba143e447cc1b503c7454f290ed0c568d6d1de94

Transactions (5)

Coinbase76fc05f74a4c05…65a8130b29f15e

1 in → 1 out9.7200 XPM110 B

AeKNrjNj…1NEq95Ta

1d33c1a151101c…a95ad39e071315

1 in → 2 out5.5965 XPM226 B

AXUavLHG…c4pfQuCq AKV5kRMX…8nfRwR2N

38030583daff0f…69becbf0204f6f

1 in → 2 out5.5785 XPM226 B

AMwAdWRw…yu6eoGKi AJuvaWSo…p92a21t4

42263a7fc4c0f0…abf591ee72c051

1 in → 2 out2.9348 XPM226 B

Aa7SV67p…KDgRgDGj AYFxzicp…jeAdgy2P

cf598ea9eee940…eb05f542eb797e

2 in → 2 out1.1316 XPM375 B

AXKm4dQB…w18XppKg AXuYPd63…5poQv3kS

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.

6.484 × 10⁹³(94-digit number)

64842283554623819096…55571415393762577539

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

6.484 × 10⁹³(94-digit number)

64842283554623819096…55571415393762577539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.484 × 10⁹³(94-digit number)

64842283554623819096…55571415393762577541

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

1.296 × 10⁹⁴(95-digit number)

12968456710924763819…11142830787525155079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.296 × 10⁹⁴(95-digit number)

12968456710924763819…11142830787525155081

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

2.593 × 10⁹⁴(95-digit number)

25936913421849527638…22285661575050310159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.593 × 10⁹⁴(95-digit number)

25936913421849527638…22285661575050310161

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

5.187 × 10⁹⁴(95-digit number)

51873826843699055276…44571323150100620319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.187 × 10⁹⁴(95-digit number)

51873826843699055276…44571323150100620321

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

1.037 × 10⁹⁵(96-digit number)

10374765368739811055…89142646300201240639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.037 × 10⁹⁵(96-digit number)

10374765368739811055…89142646300201240641

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 #334,565

Cookie Preferences