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Home/Chain Registry/Block #2,836,141

Block #2,836,141

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/12/2018, 3:06:58 PM Β· Difficulty 11.7157 Β· 4,007,814 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fabbffae38655efe18f94651092f482dbe17873255346bb97c5ce7d15dc37813
View on Chainz β†—

Difficulty

11.715718

Transactions

1

Size

200 B

Version

2

Bits

0bb73945

Nonce

1,218,291,601

Timestamp

9/12/2018, 3:06:58 PM

Confirmations

4,007,814

Merkle Root

a4c3bf532bf08548c941f92639eea99c048a2db599dcc48cf6e9233a1c927868
Transactions (1)
Coinbasea4c3bf532bf085…e9233a1c927868
1 in β†’ 1 out7.2700 XPM110 B
AaLjE4qH…P16P2aR2
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.

2.142 Γ— 10⁹⁡(96-digit number)
21428998291953563117…72942847878618887560
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.142 Γ— 10⁹⁡(96-digit number)
21428998291953563117…72942847878618887559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.285 Γ— 10⁹⁡(96-digit number)
42857996583907126235…45885695757237775119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.571 Γ— 10⁹⁡(96-digit number)
85715993167814252471…91771391514475550239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.714 Γ— 10⁹⁢(97-digit number)
17143198633562850494…83542783028951100479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.428 Γ— 10⁹⁢(97-digit number)
34286397267125700988…67085566057902200959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.857 Γ— 10⁹⁢(97-digit number)
68572794534251401977…34171132115804401919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.371 Γ— 10⁹⁷(98-digit number)
13714558906850280395…68342264231608803839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.742 Γ— 10⁹⁷(98-digit number)
27429117813700560790…36684528463217607679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.485 Γ— 10⁹⁷(98-digit number)
54858235627401121581…73369056926435215359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.097 Γ— 10⁹⁸(99-digit number)
10971647125480224316…46738113852870430719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.194 Γ— 10⁹⁸(99-digit number)
21943294250960448632…93476227705740861439
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2836141

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 fabbffae38655efe18f94651092f482dbe17873255346bb97c5ce7d15dc37813

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 #2,836,141 on Chainz β†—
Circulating Supply:57,996,016 XPMΒ·at block #6,843,954 Β· updates every 60s
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