Block #347,165

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/7/2014, 12:16:19 AM · Difficulty 10.2395 · 6,447,381 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

41d2194e07cb41446199fb2b12e7dc05f45a0e4d04066ce5e97e3236632edcdd

View on Chainz ↗

Height

#347,165

Difficulty

10.239527

Transactions

Size

724 B

Version

Bits

0a3d51a4

Nonce

114,462

Timestamp

1/7/2014, 12:16:19 AM

Confirmations

6,447,381

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

24f8b9c532454530022c360a9cfff2838a829846a73690c8a0a4558f1fd4a5a1

Transactions (2)

Coinbase438e477cc47078…621b800dbc36b0

1 in → 1 out9.5300 XPM110 B

AeKNrjNj…1NEq95Ta

40881b3e15f490…21a56220e3ede7

3 in → 2 out5.0450 XPM524 B

Aa6iq8ZD…XwBRA32e AQwcJyac…iLmLvPMc

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.

3.669 × 10⁹⁴(95-digit number)

36690517654210498708…34181451426581525819

Discovered Prime Numbers

p_k = 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.

origin − 1

3.669 × 10⁹⁴(95-digit number)

36690517654210498708…34181451426581525819

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.338 × 10⁹⁴(95-digit number)

73381035308420997416…68362902853163051639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.467 × 10⁹⁵(96-digit number)

14676207061684199483…36725805706326103279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.935 × 10⁹⁵(96-digit number)

29352414123368398966…73451611412652206559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.870 × 10⁹⁵(96-digit number)

58704828246736797933…46903222825304413119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.174 × 10⁹⁶(97-digit number)

11740965649347359586…93806445650608826239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.348 × 10⁹⁶(97-digit number)

23481931298694719173…87612891301217652479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.696 × 10⁹⁶(97-digit number)

46963862597389438346…75225782602435304959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.392 × 10⁹⁶(97-digit number)

93927725194778876693…50451565204870609919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.878 × 10⁹⁷(98-digit number)

18785545038955775338…00903130409741219839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer