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Block #6,825,840

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2026, 5:28:46 AM Β· Difficulty 10.9773 Β· 15,516 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
42ad644c5b7bd6f5a7d25ce0eda10d9cadda6b8320341bfd56a2e11c6b48b838
View on Chainz β†—

Difficulty

10.977344

Transactions

1

Size

190 B

Version

536870912

Bits

0afa333a

Nonce

2,111,190,644

Timestamp

5/5/2026, 5:28:46 AM

Confirmations

15,516

Merkle Root

eeb0b4148ba25b4c749505111edad6e92ceaf8ed7812f8f62ef377ce89cac13d
Transactions (1)
Coinbaseeeb0b4148ba25b…f377ce89cac13d
1 in β†’ 1 out8.1890 XPM101 B
AMrLYUQN…jwjifxiz
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.

3.284 Γ— 10⁹²(93-digit number)
32840688347548355800…80858883081211558360
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
3.284 Γ— 10⁹²(93-digit number)
32840688347548355800…80858883081211558361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.568 Γ— 10⁹²(93-digit number)
65681376695096711601…61717766162423116721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.313 Γ— 10⁹³(94-digit number)
13136275339019342320…23435532324846233441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.627 Γ— 10⁹³(94-digit number)
26272550678038684640…46871064649692466881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.254 Γ— 10⁹³(94-digit number)
52545101356077369281…93742129299384933761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.050 Γ— 10⁹⁴(95-digit number)
10509020271215473856…87484258598769867521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.101 Γ— 10⁹⁴(95-digit number)
21018040542430947712…74968517197539735041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.203 Γ— 10⁹⁴(95-digit number)
42036081084861895425…49937034395079470081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.407 Γ— 10⁹⁴(95-digit number)
84072162169723790850…99874068790158940161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.681 Γ— 10⁹⁡(96-digit number)
16814432433944758170…99748137580317880321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.362 Γ— 10⁹⁡(96-digit number)
33628864867889516340…99496275160635760641
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 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
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 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 6825840

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 42ad644c5b7bd6f5a7d25ce0eda10d9cadda6b8320341bfd56a2e11c6b48b838

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 #6,825,840 on Chainz β†—
Circulating Supply:57,975,216 XPMΒ·at block #6,841,355 Β· updates every 60s
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