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Home/Chain Registry/Block #2,333,409

Block #2,333,409

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2017, 4:36:30 AM Β· Difficulty 10.9228 Β· 4,507,740 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e27fc9f7319d047bd653502acf3e5b8a13cabcd9223077b1416bb5296743870e
View on Chainz β†—

Difficulty

10.922792

Transactions

1

Size

198 B

Version

2

Bits

0aec3c11

Nonce

189,306,055

Timestamp

10/12/2017, 4:36:30 AM

Confirmations

4,507,740

Merkle Root

243597253c3e29dc0c024757bb1a6b3cbc28919908a2fafea7b3dfaeb102ff78
Transactions (1)
Coinbase243597253c3e29…b3dfaeb102ff78
1 in β†’ 1 out8.3700 XPM109 B
AS8NnyXN…5AZpjs2Z
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.

1.381 Γ— 10⁹²(93-digit number)
13810961284458478382…60766143706164979760
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
1.381 Γ— 10⁹²(93-digit number)
13810961284458478382…60766143706164979761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.762 Γ— 10⁹²(93-digit number)
27621922568916956764…21532287412329959521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.524 Γ— 10⁹²(93-digit number)
55243845137833913529…43064574824659919041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.104 Γ— 10⁹³(94-digit number)
11048769027566782705…86129149649319838081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.209 Γ— 10⁹³(94-digit number)
22097538055133565411…72258299298639676161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.419 Γ— 10⁹³(94-digit number)
44195076110267130823…44516598597279352321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.839 Γ— 10⁹³(94-digit number)
88390152220534261646…89033197194558704641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.767 Γ— 10⁹⁴(95-digit number)
17678030444106852329…78066394389117409281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.535 Γ— 10⁹⁴(95-digit number)
35356060888213704658…56132788778234818561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.071 Γ— 10⁹⁴(95-digit number)
70712121776427409317…12265577556469637121
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 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
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 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 2333409

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 e27fc9f7319d047bd653502acf3e5b8a13cabcd9223077b1416bb5296743870e

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 #2,333,409 on Chainz β†—
Circulating Supply:57,973,555 XPMΒ·at block #6,841,148 Β· updates every 60s
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