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Block #292,856

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/3/2013, 11:50:44 PM Β· Difficulty 9.9904 Β· 6,533,526 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c02f5ce76a4b55c6a9a8c97b02da0bbd9334256aa2a757b580049975460bbb5f
View on Chainz β†—

Height

#292,856

Difficulty

9.990420

Transactions

1

Size

207 B

Version

2

Bits

09fd8c24

Nonce

145,311

Timestamp

12/3/2013, 11:50:44 PM

Confirmations

6,533,526

Merkle Root

bbe7aa1682a74779df85dd2a3bc8f49ae65dbf7945a6e5451763d77eb4ceb3f0
Transactions (1)
Coinbasebbe7aa1682a747…63d77eb4ceb3f0
1 in β†’ 1 out10.0000 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.

7.248 Γ— 10⁹⁡(96-digit number)
72481355819507383775…93359393526615294720
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
7.248 Γ— 10⁹⁡(96-digit number)
72481355819507383775…93359393526615294721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.449 Γ— 10⁹⁢(97-digit number)
14496271163901476755…86718787053230589441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.899 Γ— 10⁹⁢(97-digit number)
28992542327802953510…73437574106461178881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.798 Γ— 10⁹⁢(97-digit number)
57985084655605907020…46875148212922357761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.159 Γ— 10⁹⁷(98-digit number)
11597016931121181404…93750296425844715521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.319 Γ— 10⁹⁷(98-digit number)
23194033862242362808…87500592851689431041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.638 Γ— 10⁹⁷(98-digit number)
46388067724484725616…75001185703378862081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.277 Γ— 10⁹⁷(98-digit number)
92776135448969451232…50002371406757724161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.855 Γ— 10⁹⁸(99-digit number)
18555227089793890246…00004742813515448321
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 292856

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 c02f5ce76a4b55c6a9a8c97b02da0bbd9334256aa2a757b580049975460bbb5f

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 #292,856 on Chainz β†—
Circulating Supply:57,855,202 XPMΒ·at block #6,826,381 Β· updates every 60s
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