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Block #282,216

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/29/2013, 7:38:38 AM Β· Difficulty 9.9787 Β· 6,535,693 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
16bbd5478f981e596cc6ea9ba45fb96ae37fdfb6d501d3946af623bc5ce9705b
View on Chainz β†—

Height

#282,216

Difficulty

9.978651

Transactions

1

Size

209 B

Version

2

Bits

09fa88dc

Nonce

1,724

Timestamp

11/29/2013, 7:38:38 AM

Confirmations

6,535,693

Merkle Root

a69cd93a00858666c151eecfba2450f0315f01fdbb0a178f6c8860009b277c2f
Transactions (1)
Coinbasea69cd93a008586…8860009b277c2f
1 in β†’ 1 out10.0300 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.

5.656 Γ— 10¹⁰⁰(101-digit number)
56566395556523719585…40427012986341621760
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
5.656 Γ— 10¹⁰⁰(101-digit number)
56566395556523719585…40427012986341621761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.131 Γ— 10¹⁰¹(102-digit number)
11313279111304743917…80854025972683243521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.262 Γ— 10¹⁰¹(102-digit number)
22626558222609487834…61708051945366487041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.525 Γ— 10¹⁰¹(102-digit number)
45253116445218975668…23416103890732974081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.050 Γ— 10¹⁰¹(102-digit number)
90506232890437951336…46832207781465948161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.810 Γ— 10¹⁰²(103-digit number)
18101246578087590267…93664415562931896321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.620 Γ— 10¹⁰²(103-digit number)
36202493156175180534…87328831125863792641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.240 Γ— 10¹⁰²(103-digit number)
72404986312350361068…74657662251727585281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.448 Γ— 10¹⁰³(104-digit number)
14480997262470072213…49315324503455170561
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 282216

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 16bbd5478f981e596cc6ea9ba45fb96ae37fdfb6d501d3946af623bc5ce9705b

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 #282,216 on Chainz β†—
Circulating Supply:57,787,335 XPMΒ·at block #6,817,908 Β· updates every 60s
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