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Block #242,785

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/3/2013, 10:24:44 PM Β· Difficulty 9.9605 Β· 6,582,222 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f9c50ecc31cefc9bca96f75c552d74d46e6d0cfc701bc214c9b8359647ce419a
View on Chainz β†—

Height

#242,785

Difficulty

9.960549

Transactions

1

Size

209 B

Version

2

Bits

09f5e68c

Nonce

184,550,688

Timestamp

11/3/2013, 10:24:44 PM

Confirmations

6,582,222

Merkle Root

1ead26c8d719c0eb4332a6f2b5d17834612b6ce631fc185bc11995d9b5bab91d
Transactions (1)
Coinbase1ead26c8d719c0…1995d9b5bab91d
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.571 Γ— 10¹⁰²(103-digit number)
45716845776023290855…89461433733228789760
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
4.571 Γ— 10¹⁰²(103-digit number)
45716845776023290855…89461433733228789761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.143 Γ— 10¹⁰²(103-digit number)
91433691552046581710…78922867466457579521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.828 Γ— 10¹⁰³(104-digit number)
18286738310409316342…57845734932915159041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.657 Γ— 10¹⁰³(104-digit number)
36573476620818632684…15691469865830318081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.314 Γ— 10¹⁰³(104-digit number)
73146953241637265368…31382939731660636161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.462 Γ— 10¹⁰⁴(105-digit number)
14629390648327453073…62765879463321272321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.925 Γ— 10¹⁰⁴(105-digit number)
29258781296654906147…25531758926642544641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.851 Γ— 10¹⁰⁴(105-digit number)
58517562593309812294…51063517853285089281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.170 Γ— 10¹⁰⁡(106-digit number)
11703512518661962458…02127035706570178561
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 242785

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 f9c50ecc31cefc9bca96f75c552d74d46e6d0cfc701bc214c9b8359647ce419a

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 #242,785 on Chainz β†—
Circulating Supply:57,844,140 XPMΒ·at block #6,825,006 Β· updates every 60s
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