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Home/Chain Registry/Block #2,872,841

Block #2,872,841

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/8/2018, 5:07:09 PM Β· Difficulty 11.6643 Β· 3,969,624 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3c3918aba1e48bc61e4dbae631264bb0ce229c43ae9d4400d80a4a21fa43f7b4
View on Chainz β†—

Difficulty

11.664297

Transactions

1

Size

201 B

Version

2

Bits

0baa0f5e

Nonce

1,646,340,417

Timestamp

10/8/2018, 5:07:09 PM

Confirmations

3,969,624

Merkle Root

3bfd42f5e28f9084ff2f4cbb86eea73eb3c88ee358cb8134ea1eaf33605e3774
Transactions (1)
Coinbase3bfd42f5e28f90…1eaf33605e3774
1 in β†’ 1 out7.3400 XPM110 B
AUMQRepm…tAfKmdW1
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.

3.290 Γ— 10⁹⁢(97-digit number)
32909753576349467503…17791090238287216640
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
3.290 Γ— 10⁹⁢(97-digit number)
32909753576349467503…17791090238287216639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.581 Γ— 10⁹⁢(97-digit number)
65819507152698935006…35582180476574433279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.316 Γ— 10⁹⁷(98-digit number)
13163901430539787001…71164360953148866559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.632 Γ— 10⁹⁷(98-digit number)
26327802861079574002…42328721906297733119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.265 Γ— 10⁹⁷(98-digit number)
52655605722159148004…84657443812595466239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.053 Γ— 10⁹⁸(99-digit number)
10531121144431829600…69314887625190932479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.106 Γ— 10⁹⁸(99-digit number)
21062242288863659201…38629775250381864959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.212 Γ— 10⁹⁸(99-digit number)
42124484577727318403…77259550500763729919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.424 Γ— 10⁹⁸(99-digit number)
84248969155454636807…54519101001527459839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.684 Γ— 10⁹⁹(100-digit number)
16849793831090927361…09038202003054919679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.369 Γ— 10⁹⁹(100-digit number)
33699587662181854723…18076404006109839359
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 2872841

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 3c3918aba1e48bc61e4dbae631264bb0ce229c43ae9d4400d80a4a21fa43f7b4

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 #2,872,841 on Chainz β†—
Circulating Supply:57,984,138 XPMΒ·at block #6,842,464 Β· updates every 60s
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