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Block #2,234,586

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/3/2017, 3:28:07 AM Β· Difficulty 10.9457 Β· 4,609,271 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
afac509fc9e1ab9333d7c09bea44397fd1c6c05216d321d2833bdc7cafba2479
View on Chainz β†—

Difficulty

10.945682

Transactions

1

Size

199 B

Version

2

Bits

0af21836

Nonce

1,722,035,428

Timestamp

8/3/2017, 3:28:07 AM

Confirmations

4,609,271

Merkle Root

9eddd73592b78381c6b2e016a8f8d2ba9ac8a6ee6b4218b637b77f4572673150
Transactions (1)
Coinbase9eddd73592b783…b77f4572673150
1 in β†’ 1 out8.3300 XPM110 B
APcB9cJT…5RfQz5st
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.

1.300 Γ— 10⁹²(93-digit number)
13002406608775677788…36799213474155854080
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
1.300 Γ— 10⁹²(93-digit number)
13002406608775677788…36799213474155854079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.600 Γ— 10⁹²(93-digit number)
26004813217551355576…73598426948311708159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.200 Γ— 10⁹²(93-digit number)
52009626435102711152…47196853896623416319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.040 Γ— 10⁹³(94-digit number)
10401925287020542230…94393707793246832639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.080 Γ— 10⁹³(94-digit number)
20803850574041084460…88787415586493665279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.160 Γ— 10⁹³(94-digit number)
41607701148082168921…77574831172987330559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.321 Γ— 10⁹³(94-digit number)
83215402296164337843…55149662345974661119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.664 Γ— 10⁹⁴(95-digit number)
16643080459232867568…10299324691949322239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.328 Γ— 10⁹⁴(95-digit number)
33286160918465735137…20598649383898644479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.657 Γ— 10⁹⁴(95-digit number)
66572321836931470274…41197298767797288959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.331 Γ— 10⁹⁡(96-digit number)
13314464367386294054…82394597535594577919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2234586

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 afac509fc9e1ab9333d7c09bea44397fd1c6c05216d321d2833bdc7cafba2479

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 #2,234,586 on Chainz β†—
Circulating Supply:57,995,224 XPMΒ·at block #6,843,856 Β· updates every 60s
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