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Block #222,217

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/22/2013, 1:45:42 AM Β· Difficulty 9.9399 Β· 6,573,879 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
05bb61ed73dabb001f3891245b07b4e7bd8c4a7ff2a00e143be21a86672dad45
View on Chainz β†—

Height

#222,217

Difficulty

9.939855

Transactions

1

Size

211 B

Version

2

Bits

09f09a58

Nonce

203

Timestamp

10/22/2013, 1:45:42 AM

Confirmations

6,573,879

Merkle Root

037fa7fa60ea06adc069297165596dbf1dfc24fefaafad18cf7a020cba4898ca
Transactions (1)
Coinbase037fa7fa60ea06…7a020cba4898ca
1 in β†’ 1 out10.1100 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.

3.161 Γ— 10¹⁰⁷(108-digit number)
31612167108556950610…39685860020326323200
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.161 Γ— 10¹⁰⁷(108-digit number)
31612167108556950610…39685860020326323199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.322 Γ— 10¹⁰⁷(108-digit number)
63224334217113901220…79371720040652646399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.264 Γ— 10¹⁰⁸(109-digit number)
12644866843422780244…58743440081305292799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.528 Γ— 10¹⁰⁸(109-digit number)
25289733686845560488…17486880162610585599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.057 Γ— 10¹⁰⁸(109-digit number)
50579467373691120976…34973760325221171199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.011 Γ— 10¹⁰⁹(110-digit number)
10115893474738224195…69947520650442342399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.023 Γ— 10¹⁰⁹(110-digit number)
20231786949476448390…39895041300884684799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.046 Γ— 10¹⁰⁹(110-digit number)
40463573898952896781…79790082601769369599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.092 Γ— 10¹⁰⁹(110-digit number)
80927147797905793562…59580165203538739199
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 222217

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 05bb61ed73dabb001f3891245b07b4e7bd8c4a7ff2a00e143be21a86672dad45

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 #222,217 on Chainz β†—
Circulating Supply:57,612,768 XPMΒ·at block #6,796,095 Β· updates every 60s
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