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Home/Chain Registry/Block #2,833,005

Block #2,833,005

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 11:05:03 AM Β· Difficulty 11.7148 Β· 4,007,458 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb843865d61b8a5fd2b1cf3fdb41b3ecb1d9eb9475d7fd2dfe02e6c240356750
View on Chainz β†—

Difficulty

11.714806

Transactions

1

Size

201 B

Version

2

Bits

0bb6fd8c

Nonce

1,188,378,588

Timestamp

9/10/2018, 11:05:03 AM

Confirmations

4,007,458

Merkle Root

cbf1d836fd68fda367cf31f454b4ab706b3e96c36d31922d84510c1bc1fb5175
Transactions (1)
Coinbasecbf1d836fd68fd…510c1bc1fb5175
1 in β†’ 1 out7.2700 XPM110 B
AJNDwzhq…W24Su2sj
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.

1.135 Γ— 10⁹⁢(97-digit number)
11357830571019123310…04327526059308461120
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
1.135 Γ— 10⁹⁢(97-digit number)
11357830571019123310…04327526059308461121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.271 Γ— 10⁹⁢(97-digit number)
22715661142038246621…08655052118616922241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.543 Γ— 10⁹⁢(97-digit number)
45431322284076493243…17310104237233844481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.086 Γ— 10⁹⁢(97-digit number)
90862644568152986486…34620208474467688961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.817 Γ— 10⁹⁷(98-digit number)
18172528913630597297…69240416948935377921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.634 Γ— 10⁹⁷(98-digit number)
36345057827261194594…38480833897870755841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.269 Γ— 10⁹⁷(98-digit number)
72690115654522389188…76961667795741511681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.453 Γ— 10⁹⁸(99-digit number)
14538023130904477837…53923335591483023361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.907 Γ— 10⁹⁸(99-digit number)
29076046261808955675…07846671182966046721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.815 Γ— 10⁹⁸(99-digit number)
58152092523617911351…15693342365932093441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.163 Γ— 10⁹⁹(100-digit number)
11630418504723582270…31386684731864186881
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 2833005

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 cb843865d61b8a5fd2b1cf3fdb41b3ecb1d9eb9475d7fd2dfe02e6c240356750

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 #2,833,005 on Chainz β†—
Circulating Supply:57,968,032 XPMΒ·at block #6,840,462 Β· updates every 60s
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