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Home/Chain Registry/Block #2,634,149

Block #2,634,149

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 6:57:31 PM Β· Difficulty 11.2259 Β· 4,210,775 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a1bc9ae44f66feb6853cf99ea72c87922c1f6838bf7a24be7e232089603f6800
View on Chainz β†—

Difficulty

11.225904

Transactions

1

Size

199 B

Version

2

Bits

0b39d4da

Nonce

2,135,467,187

Timestamp

4/28/2018, 6:57:31 PM

Confirmations

4,210,775

Merkle Root

6d9a72c3b07a8a3b37bc750277d8a295ccffe64c340d3708ee99f5121f5ea900
Transactions (1)
Coinbase6d9a72c3b07a8a…99f5121f5ea900
1 in β†’ 1 out7.9200 XPM109 B
AM59a5f8…ciB8nUEx
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.

1.112 Γ— 10⁹⁡(96-digit number)
11126561200182034417…94173224972253184000
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
1.112 Γ— 10⁹⁡(96-digit number)
11126561200182034417…94173224972253183999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.225 Γ— 10⁹⁡(96-digit number)
22253122400364068835…88346449944506367999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.450 Γ— 10⁹⁡(96-digit number)
44506244800728137671…76692899889012735999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.901 Γ— 10⁹⁡(96-digit number)
89012489601456275342…53385799778025471999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.780 Γ— 10⁹⁢(97-digit number)
17802497920291255068…06771599556050943999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.560 Γ— 10⁹⁢(97-digit number)
35604995840582510136…13543199112101887999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.120 Γ— 10⁹⁢(97-digit number)
71209991681165020273…27086398224203775999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.424 Γ— 10⁹⁷(98-digit number)
14241998336233004054…54172796448407551999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.848 Γ— 10⁹⁷(98-digit number)
28483996672466008109…08345592896815103999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.696 Γ— 10⁹⁷(98-digit number)
56967993344932016218…16691185793630207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.139 Γ— 10⁹⁸(99-digit number)
11393598668986403243…33382371587260415999
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 2634149

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 a1bc9ae44f66feb6853cf99ea72c87922c1f6838bf7a24be7e232089603f6800

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 #2,634,149 on Chainz β†—
Circulating Supply:58,003,810 XPMΒ·at block #6,844,923 Β· updates every 60s
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