Block #345,755

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/6/2014, 3:31:17 AM · Difficulty 10.2133 · 6,467,224 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

19799db099de9887b2d2bfadb3cf0f0815b0fd71d6ff77d4e4b5836274067bb8

View on Chainz ↗

Height

#345,755

Difficulty

10.213289

Transactions

Size

1.51 KB

Version

Bits

0a369a22

Nonce

59,883

Timestamp

1/6/2014, 3:31:17 AM

Confirmations

6,467,224

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

081aecf55da40bae1219e705d883fd038d2e07c9fba018f2567676798c7c1dd7

Transactions (3)

Coinbase1813f7293ac669…02ace64d971e2b

1 in → 1 out9.6000 XPM110 B

AeKNrjNj…1NEq95Ta

0a0274032cec83…55ed31f2c9d8d9

7 in → 2 out2.1292 XPM1.09 KB

ATBbLgj2…ybDRYymh AYW2CJyb…6a1kwSEb

6f2594ff4089e9…9e4008df714ef3

1 in → 2 out1.5868 XPM226 B

AdiAcsDb…ny9MCogr AWj3A8PZ…f8yENJqo

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.

3.435 × 10¹⁰²(103-digit number)

34350880314899545585…26035667284133821439

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

3.435 × 10¹⁰²(103-digit number)

34350880314899545585…26035667284133821439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.435 × 10¹⁰²(103-digit number)

34350880314899545585…26035667284133821441

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

6.870 × 10¹⁰²(103-digit number)

68701760629799091171…52071334568267642879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.870 × 10¹⁰²(103-digit number)

68701760629799091171…52071334568267642881

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

1.374 × 10¹⁰³(104-digit number)

13740352125959818234…04142669136535285759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.374 × 10¹⁰³(104-digit number)

13740352125959818234…04142669136535285761

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

2.748 × 10¹⁰³(104-digit number)

27480704251919636468…08285338273070571519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.748 × 10¹⁰³(104-digit number)

27480704251919636468…08285338273070571521

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

5.496 × 10¹⁰³(104-digit number)

54961408503839272937…16570676546141143039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.496 × 10¹⁰³(104-digit number)

54961408503839272937…16570676546141143041

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 #345,755

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