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Block #2,233,250

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/2/2017, 4:27:26 AM Β· Difficulty 10.9461 Β· 4,604,484 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b6002f6b4a232bfdd006a2e5b07803d9c7b2d0dc5716cde59b33046491a33206
View on Chainz β†—

Difficulty

10.946121

Transactions

1

Size

200 B

Version

2

Bits

0af234fc

Nonce

1,454,725,251

Timestamp

8/2/2017, 4:27:26 AM

Confirmations

4,604,484

Merkle Root

21135a3e9f83eafc927a9c7bcdb405c83ccdea48caaa000e6c0192a839927dd1
Transactions (1)
Coinbase21135a3e9f83ea…0192a839927dd1
1 in β†’ 1 out8.3300 XPM110 B
AKdS2EdC…5fLRWccQ
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.

1.912 Γ— 10⁹⁡(96-digit number)
19129424109046040343…92079641708637440000
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
1.912 Γ— 10⁹⁡(96-digit number)
19129424109046040343…92079641708637439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.825 Γ— 10⁹⁡(96-digit number)
38258848218092080686…84159283417274879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.651 Γ— 10⁹⁡(96-digit number)
76517696436184161373…68318566834549759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.530 Γ— 10⁹⁢(97-digit number)
15303539287236832274…36637133669099519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.060 Γ— 10⁹⁢(97-digit number)
30607078574473664549…73274267338199039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.121 Γ— 10⁹⁢(97-digit number)
61214157148947329098…46548534676398079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.224 Γ— 10⁹⁷(98-digit number)
12242831429789465819…93097069352796159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.448 Γ— 10⁹⁷(98-digit number)
24485662859578931639…86194138705592319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.897 Γ— 10⁹⁷(98-digit number)
48971325719157863279…72388277411184639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.794 Γ— 10⁹⁷(98-digit number)
97942651438315726558…44776554822369279999
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 2233250

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 b6002f6b4a232bfdd006a2e5b07803d9c7b2d0dc5716cde59b33046491a33206

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 #2,233,250 on Chainz β†—
Circulating Supply:57,946,204 XPMΒ·at block #6,837,733 Β· updates every 60s
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