Block #353,449

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2014, 10:55:11 PM · Difficulty 10.3268 · 6,463,371 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

692a4957592d96689604a6867779632ae1a108068d7391ae69838e4ebca13524

View on Chainz ↗

Height

#353,449

Difficulty

10.326771

Transactions

Size

1.08 KB

Version

Bits

0a53a747

Nonce

1,220,129

Timestamp

1/10/2014, 10:55:11 PM

Confirmations

6,463,371

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2583868b523579381c7e300f2474a77094e85f3114b21c136069d10a0fc4eaf2

Transactions (5)

Coinbasebf3689d4ca04e0…a8ef7ca0c8363c

1 in → 1 out9.4000 XPM110 B

AeKNrjNj…1NEq95Ta

949c1a7a837fbe…8b6e8b6c177d8c

1 in → 2 out4.6043 XPM225 B

ALv4RXXo…j4XJgzRe APir8rMg…GqVAYtkU

561ea95cb528fc…6be9155b1b97cf

1 in → 2 out4.3338 XPM225 B

AbNi5BNi…t3dPAa73 ANECpbxd…XLvANQZs

4572ff5fb2f200…a87abbe749d5cd

1 in → 2 out1.4117 XPM226 B

AK3yL9WG…kWY2xQa4 AZiEiDJa…L3u12nfr

286d1310d16778…18cfad78520ab0

1 in → 2 out1.3086 XPM226 B

AavM9ADQ…s5wFV2jY AXUciLCx…HgTFhZu5

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.

3.096 × 10⁹⁹(100-digit number)

30968304174587385901…66429611689754836799

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

3.096 × 10⁹⁹(100-digit number)

30968304174587385901…66429611689754836799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.096 × 10⁹⁹(100-digit number)

30968304174587385901…66429611689754836801

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

6.193 × 10⁹⁹(100-digit number)

61936608349174771803…32859223379509673599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.193 × 10⁹⁹(100-digit number)

61936608349174771803…32859223379509673601

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

1.238 × 10¹⁰⁰(101-digit number)

12387321669834954360…65718446759019347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.238 × 10¹⁰⁰(101-digit number)

12387321669834954360…65718446759019347201

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

2.477 × 10¹⁰⁰(101-digit number)

24774643339669908721…31436893518038694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.477 × 10¹⁰⁰(101-digit number)

24774643339669908721…31436893518038694401

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

4.954 × 10¹⁰⁰(101-digit number)

49549286679339817442…62873787036077388799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.954 × 10¹⁰⁰(101-digit number)

49549286679339817442…62873787036077388801

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 #353,449

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