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Block #183,548

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/28/2013, 2:21:52 AM Β· Difficulty 9.8579 Β· 6,643,778 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
27619882cea3ae1e4f7ac000db921b0db3cbc052368bbb84ddf9b86d14aba2df
View on Chainz β†—

Height

#183,548

Difficulty

9.857948

Transactions

1

Size

199 B

Version

2

Bits

09dba274

Nonce

293,439

Timestamp

9/28/2013, 2:21:52 AM

Confirmations

6,643,778

Merkle Root

4051d219fb8eed277be7794d3454c5584d66af843edd58da31e3e1269dcfaec7
Transactions (1)
Coinbase4051d219fb8eed…e3e1269dcfaec7
1 in β†’ 1 out10.2700 XPM109 B
AWsEijaA…9WbDL6tH
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.355 Γ— 10⁹⁴(95-digit number)
23554981084787097259…17659499480770746560
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
2.355 Γ— 10⁹⁴(95-digit number)
23554981084787097259…17659499480770746561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.710 Γ— 10⁹⁴(95-digit number)
47109962169574194518…35318998961541493121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.421 Γ— 10⁹⁴(95-digit number)
94219924339148389037…70637997923082986241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.884 Γ— 10⁹⁡(96-digit number)
18843984867829677807…41275995846165972481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.768 Γ— 10⁹⁡(96-digit number)
37687969735659355615…82551991692331944961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.537 Γ— 10⁹⁡(96-digit number)
75375939471318711230…65103983384663889921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.507 Γ— 10⁹⁢(97-digit number)
15075187894263742246…30207966769327779841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.015 Γ— 10⁹⁢(97-digit number)
30150375788527484492…60415933538655559681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.030 Γ— 10⁹⁢(97-digit number)
60300751577054968984…20831867077311119361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” 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 β†’
β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 183548

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 27619882cea3ae1e4f7ac000db921b0db3cbc052368bbb84ddf9b86d14aba2df

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 β†’ Debug Window β†’ 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 #183,548 on Chainz β†—
Circulating Supply:57,862,721 XPMΒ·at block #6,827,325 Β· updates every 60s
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