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Home/Chain Registry/Block #286,826

Block #286,826

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/1/2013, 1:27:21 AM Β· Difficulty 9.9860 Β· 6,514,014 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3dfa8b1cb0244de9d25550c76baad48ed27fa407d9baf5cbb0358d5ea79da143
View on Chainz β†—

Height

#286,826

Difficulty

9.986048

Transactions

1

Size

208 B

Version

2

Bits

09fc6da8

Nonce

28,445

Timestamp

12/1/2013, 1:27:21 AM

Confirmations

6,514,014

Merkle Root

58889990a8db07e095d73aa38b1b15daa37ee1725ef2af4507f061669edfa69c
Transactions (1)
Coinbase58889990a8db07…f061669edfa69c
1 in β†’ 1 out10.0100 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.

1.846 Γ— 10⁹⁹(100-digit number)
18468530262311825429…68194612860266606040
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
1.846 Γ— 10⁹⁹(100-digit number)
18468530262311825429…68194612860266606041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.693 Γ— 10⁹⁹(100-digit number)
36937060524623650859…36389225720533212081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.387 Γ— 10⁹⁹(100-digit number)
73874121049247301718…72778451441066424161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.477 Γ— 10¹⁰⁰(101-digit number)
14774824209849460343…45556902882132848321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.954 Γ— 10¹⁰⁰(101-digit number)
29549648419698920687…91113805764265696641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.909 Γ— 10¹⁰⁰(101-digit number)
59099296839397841374…82227611528531393281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.181 Γ— 10¹⁰¹(102-digit number)
11819859367879568274…64455223057062786561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.363 Γ— 10¹⁰¹(102-digit number)
23639718735759136549…28910446114125573121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.727 Γ— 10¹⁰¹(102-digit number)
47279437471518273099…57820892228251146241
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 286826

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 3dfa8b1cb0244de9d25550c76baad48ed27fa407d9baf5cbb0358d5ea79da143

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 #286,826 on Chainz β†—
Circulating Supply:57,650,778 XPMΒ·at block #6,800,839 Β· updates every 60s
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