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Block #322,385

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/20/2013, 11:18:25 PM Β· Difficulty 10.1946 Β· 6,503,204 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cfebd0a288b168e00b53fb4b50bfa30a07deecf1a9e3b5ef0e78853b98fa682a
View on Chainz β†—

Height

#322,385

Difficulty

10.194626

Transactions

1

Size

207 B

Version

2

Bits

0a31d300

Nonce

33,556,301

Timestamp

12/20/2013, 11:18:25 PM

Confirmations

6,503,204

Merkle Root

2bf96747dd428e58b7355e5d29a789743376f3ef42a3f5d92898736d94ded5fb
Transactions (1)
Coinbase2bf96747dd428e…98736d94ded5fb
1 in β†’ 1 out9.6100 XPM116 B
AbwWkWZt…kawDhufa
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.

1.038 Γ— 10⁹⁷(98-digit number)
10380537019278871438…05058728314329552400
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
1.038 Γ— 10⁹⁷(98-digit number)
10380537019278871438…05058728314329552399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.076 Γ— 10⁹⁷(98-digit number)
20761074038557742877…10117456628659104799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.152 Γ— 10⁹⁷(98-digit number)
41522148077115485754…20234913257318209599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.304 Γ— 10⁹⁷(98-digit number)
83044296154230971509…40469826514636419199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.660 Γ— 10⁹⁸(99-digit number)
16608859230846194301…80939653029272838399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.321 Γ— 10⁹⁸(99-digit number)
33217718461692388603…61879306058545676799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.643 Γ— 10⁹⁸(99-digit number)
66435436923384777207…23758612117091353599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.328 Γ— 10⁹⁹(100-digit number)
13287087384676955441…47517224234182707199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.657 Γ— 10⁹⁹(100-digit number)
26574174769353910882…95034448468365414399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.314 Γ— 10⁹⁹(100-digit number)
53148349538707821765…90068896936730828799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 322385

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 cfebd0a288b168e00b53fb4b50bfa30a07deecf1a9e3b5ef0e78853b98fa682a

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 #322,385 on Chainz β†—
Circulating Supply:57,848,812 XPMΒ·at block #6,825,588 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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