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Home/Chain Registry/Block #2,861,196

Block #2,861,196

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/30/2018, 12:10:21 PM Β· Difficulty 11.6751 Β· 3,971,746 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7842ac7b5b78af12c09f2f73127aabd98f0161b7f156c44fb562f5c1235a8b39
View on Chainz β†—

Difficulty

11.675085

Transactions

1

Size

200 B

Version

2

Bits

0bacd25a

Nonce

1,345,410,412

Timestamp

9/30/2018, 12:10:21 PM

Confirmations

3,971,746

Merkle Root

2fb11b5968476831974b6dff5188500a03289bf32d7f211413bf1e991dde055d
Transactions (1)
Coinbase2fb11b59684768…bf1e991dde055d
1 in β†’ 1 out7.3200 XPM110 B
AHaEZ111…DGKaBwDb
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.

1.096 Γ— 10⁹⁴(95-digit number)
10965997219430340438…68263661648156887040
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
1.096 Γ— 10⁹⁴(95-digit number)
10965997219430340438…68263661648156887041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.193 Γ— 10⁹⁴(95-digit number)
21931994438860680876…36527323296313774081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.386 Γ— 10⁹⁴(95-digit number)
43863988877721361752…73054646592627548161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.772 Γ— 10⁹⁴(95-digit number)
87727977755442723505…46109293185255096321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.754 Γ— 10⁹⁡(96-digit number)
17545595551088544701…92218586370510192641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.509 Γ— 10⁹⁡(96-digit number)
35091191102177089402…84437172741020385281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.018 Γ— 10⁹⁡(96-digit number)
70182382204354178804…68874345482040770561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.403 Γ— 10⁹⁢(97-digit number)
14036476440870835760…37748690964081541121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.807 Γ— 10⁹⁢(97-digit number)
28072952881741671521…75497381928163082241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.614 Γ— 10⁹⁢(97-digit number)
56145905763483343043…50994763856326164481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.122 Γ— 10⁹⁷(98-digit number)
11229181152696668608…01989527712652328961
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 2861196

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 7842ac7b5b78af12c09f2f73127aabd98f0161b7f156c44fb562f5c1235a8b39

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 #2,861,196 on Chainz β†—
Circulating Supply:57,907,714 XPMΒ·at block #6,832,941 Β· updates every 60s
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