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Home/Chain Registry/Block #2,833,237

Block #2,833,237

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 2:45:55 PM Β· Difficulty 11.7154 Β· 4,008,439 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
444da4b828e16b9e1e6da28fb9f4d51bc0f73ea0fd3600985e0768c8103558bd
View on Chainz β†—

Difficulty

11.715383

Transactions

1

Size

200 B

Version

2

Bits

0bb7235d

Nonce

1,098,726,535

Timestamp

9/10/2018, 2:45:55 PM

Confirmations

4,008,439

Merkle Root

9c3d5919da45e6329044ea67eeaaeb24783b5c5588eb464f356f8e686a3d1b6e
Transactions (1)
Coinbase9c3d5919da45e6…6f8e686a3d1b6e
1 in β†’ 1 out7.2700 XPM110 B
AKe7uLHH…Vx3Xd7j3
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.

3.425 Γ— 10⁹⁴(95-digit number)
34251344308503073926…92048804164674861200
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
3.425 Γ— 10⁹⁴(95-digit number)
34251344308503073926…92048804164674861201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.850 Γ— 10⁹⁴(95-digit number)
68502688617006147853…84097608329349722401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.370 Γ— 10⁹⁡(96-digit number)
13700537723401229570…68195216658699444801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.740 Γ— 10⁹⁡(96-digit number)
27401075446802459141…36390433317398889601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.480 Γ— 10⁹⁡(96-digit number)
54802150893604918283…72780866634797779201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.096 Γ— 10⁹⁢(97-digit number)
10960430178720983656…45561733269595558401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.192 Γ— 10⁹⁢(97-digit number)
21920860357441967313…91123466539191116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.384 Γ— 10⁹⁢(97-digit number)
43841720714883934626…82246933078382233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.768 Γ— 10⁹⁢(97-digit number)
87683441429767869252…64493866156764467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.753 Γ— 10⁹⁷(98-digit number)
17536688285953573850…28987732313528934401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.507 Γ— 10⁹⁷(98-digit number)
35073376571907147701…57975464627057868801
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 2833237

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 444da4b828e16b9e1e6da28fb9f4d51bc0f73ea0fd3600985e0768c8103558bd

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 #2,833,237 on Chainz β†—
Circulating Supply:57,977,796 XPMΒ·at block #6,841,675 Β· updates every 60s
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