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Home/Chain Registry/Block #2,142,711

Block #2,142,711

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2017, 12:48:10 AM Β· Difficulty 10.8777 Β· 4,690,094 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bd55a2e68185744028787681a88cf930ed3d9eb8b7d2cacc0507d7c7f1f604d2
View on Chainz β†—

Difficulty

10.877695

Transactions

1

Size

199 B

Version

2

Bits

0ae0b09e

Nonce

112,151,431

Timestamp

6/3/2017, 12:48:10 AM

Confirmations

4,690,094

Merkle Root

d16b9fb3100ee54344391e5287242f05e54e51b22f0c4028ca21dba58eff627c
Transactions (1)
Coinbased16b9fb3100ee5…21dba58eff627c
1 in β†’ 1 out8.4400 XPM109 B
AQht5H5s…dBMZbeNb
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.

4.730 Γ— 10⁹⁴(95-digit number)
47308926884711035538…22192599139801392920
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
4.730 Γ— 10⁹⁴(95-digit number)
47308926884711035538…22192599139801392921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.461 Γ— 10⁹⁴(95-digit number)
94617853769422071077…44385198279602785841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.892 Γ— 10⁹⁡(96-digit number)
18923570753884414215…88770396559205571681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.784 Γ— 10⁹⁡(96-digit number)
37847141507768828431…77540793118411143361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.569 Γ— 10⁹⁡(96-digit number)
75694283015537656862…55081586236822286721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.513 Γ— 10⁹⁢(97-digit number)
15138856603107531372…10163172473644573441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.027 Γ— 10⁹⁢(97-digit number)
30277713206215062744…20326344947289146881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.055 Γ— 10⁹⁢(97-digit number)
60555426412430125489…40652689894578293761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.211 Γ— 10⁹⁷(98-digit number)
12111085282486025097…81305379789156587521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.422 Γ— 10⁹⁷(98-digit number)
24222170564972050195…62610759578313175041
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 2142711

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 bd55a2e68185744028787681a88cf930ed3d9eb8b7d2cacc0507d7c7f1f604d2

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 #2,142,711 on Chainz β†—
Circulating Supply:57,906,610 XPMΒ·at block #6,832,804 Β· updates every 60s
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