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Block #2,136,227

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/28/2017, 11:31:10 PM Β· Difficulty 10.8953 Β· 4,704,818 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
50972373d533e713c967f280c859c94e33358319934ac0bfcef550958d81bb34
View on Chainz β†—

Difficulty

10.895268

Transactions

1

Size

201 B

Version

2

Bits

0ae5304a

Nonce

463,505,103

Timestamp

5/28/2017, 11:31:10 PM

Confirmations

4,704,818

Merkle Root

01029a99ebafd8e22d41ef58205133960c9c8a3b92eb0e3397b8b452dc7ac09d
Transactions (1)
Coinbase01029a99ebafd8…b8b452dc7ac09d
1 in β†’ 1 out8.4100 XPM110 B
AZ2EQ3YE…7LWnCLu8
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.

5.552 Γ— 10⁹⁢(97-digit number)
55523058501284890432…07093076898690165760
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
5.552 Γ— 10⁹⁢(97-digit number)
55523058501284890432…07093076898690165761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.110 Γ— 10⁹⁷(98-digit number)
11104611700256978086…14186153797380331521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.220 Γ— 10⁹⁷(98-digit number)
22209223400513956172…28372307594760663041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.441 Γ— 10⁹⁷(98-digit number)
44418446801027912345…56744615189521326081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.883 Γ— 10⁹⁷(98-digit number)
88836893602055824691…13489230379042652161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.776 Γ— 10⁹⁸(99-digit number)
17767378720411164938…26978460758085304321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.553 Γ— 10⁹⁸(99-digit number)
35534757440822329876…53956921516170608641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.106 Γ— 10⁹⁸(99-digit number)
71069514881644659753…07913843032341217281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.421 Γ— 10⁹⁹(100-digit number)
14213902976328931950…15827686064682434561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.842 Γ— 10⁹⁹(100-digit number)
28427805952657863901…31655372129364869121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.685 Γ— 10⁹⁹(100-digit number)
56855611905315727802…63310744258729738241
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 2136227

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 50972373d533e713c967f280c859c94e33358319934ac0bfcef550958d81bb34

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 #2,136,227 on Chainz β†—
Circulating Supply:57,972,722 XPMΒ·at block #6,841,044 Β· updates every 60s
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