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Block #848,592

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2014, 5:01:09 AM · Difficulty 10.9716 · 5,995,820 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4e2e0037f6f7842fd6a3023a6c06f03b68d99bf4aeda2ea92e90d573f4dcc5fd

View on Chainz ↗

Height

#848,592

Difficulty

10.971562

Transactions

Size

886 B

Version

Bits

0af8b843

Nonce

1,309,278,328

Timestamp

12/11/2014, 5:01:09 AM

Confirmations

5,995,820

Merkle Root

a9ec0c6d7c4eb8236155c0267d2345f0f578d1f7c6a0e3e4499fa2067333baa5

Transactions (4)

Coinbase710cf7180d8b50…b16c95b3a0b224

1 in → 1 out8.3250 XPM116 B

ANSXnLY2…Sd25TjkD

e552e8d3d6a8cb…80390e96c43d84

1 in → 2 out4.2850 XPM226 B

APyTqNaG…k8o345ff ATSzBHPt…3E9Qo6BM

c339ad88cf8649…f122faa25298e3

1 in → 2 out4.2850 XPM226 B

AMN6qDkt…VuvvTq6f AH4dqn8s…r9NRhBU2

ec5cbf6aa9de93…9375203f831ff7

1 in → 2 out0.1238 XPM227 B

AGKP9Xpo…gagtwwx8 Abu4NCpR…kYb8nFRQ

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.

4.092 × 10⁹⁷(98-digit number)

40928678447380751485…62036118078580776960

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

4.092 × 10⁹⁷(98-digit number)

40928678447380751485…62036118078580776961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.185 × 10⁹⁷(98-digit number)

81857356894761502971…24072236157161553921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.637 × 10⁹⁸(99-digit number)

16371471378952300594…48144472314323107841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.274 × 10⁹⁸(99-digit number)

32742942757904601188…96288944628646215681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.548 × 10⁹⁸(99-digit number)

65485885515809202377…92577889257292431361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.309 × 10⁹⁹(100-digit number)

13097177103161840475…85155778514584862721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.619 × 10⁹⁹(100-digit number)

26194354206323680951…70311557029169725441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.238 × 10⁹⁹(100-digit number)

52388708412647361902…40623114058339450881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.047 × 10¹⁰⁰(101-digit number)

10477741682529472380…81246228116678901761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.095 × 10¹⁰⁰(101-digit number)

20955483365058944760…62492456233357803521

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 Second 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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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 2CC formula:

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 848592

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 4e2e0037f6f7842fd6a3023a6c06f03b68d99bf4aeda2ea92e90d573f4dcc5fd

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #848,592 on Chainz ↗

Block #848,592

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