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Home/Chain Registry/Block #3,363,211

Block #3,363,211

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/21/2019, 2:58:09 AM Β· Difficulty 10.9956 Β· 3,453,419 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
32398032b3dc26a03f3f312be55e2438ab7fa539ee2d97fa3126600a60eb2b0a
View on Chainz β†—

Difficulty

10.995591

Transactions

1

Size

200 B

Version

2

Bits

0afedf0e

Nonce

1,735,188,541

Timestamp

9/21/2019, 2:58:09 AM

Confirmations

3,453,419

Merkle Root

92c5722db5d8476d7e583a0af6356a34c0d6984ea0766d655259a8185460a9ce
Transactions (1)
Coinbase92c5722db5d847…59a8185460a9ce
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

1.818 Γ— 10⁹⁡(96-digit number)
18187600060344296477…88715451678596310400
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
1.818 Γ— 10⁹⁡(96-digit number)
18187600060344296477…88715451678596310399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.637 Γ— 10⁹⁡(96-digit number)
36375200120688592954…77430903357192620799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.275 Γ— 10⁹⁡(96-digit number)
72750400241377185908…54861806714385241599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.455 Γ— 10⁹⁢(97-digit number)
14550080048275437181…09723613428770483199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.910 Γ— 10⁹⁢(97-digit number)
29100160096550874363…19447226857540966399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.820 Γ— 10⁹⁢(97-digit number)
58200320193101748726…38894453715081932799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.164 Γ— 10⁹⁷(98-digit number)
11640064038620349745…77788907430163865599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.328 Γ— 10⁹⁷(98-digit number)
23280128077240699490…55577814860327731199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.656 Γ— 10⁹⁷(98-digit number)
46560256154481398981…11155629720655462399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.312 Γ— 10⁹⁷(98-digit number)
93120512308962797962…22311259441310924799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.862 Γ— 10⁹⁸(99-digit number)
18624102461792559592…44622518882621849599
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 3363211

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 32398032b3dc26a03f3f312be55e2438ab7fa539ee2d97fa3126600a60eb2b0a

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 #3,363,211 on Chainz β†—
Circulating Supply:57,777,154 XPMΒ·at block #6,816,629 Β· updates every 60s
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