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Home/Chain Registry/Block #3,284,073

Block #3,284,073

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/27/2019, 5:13:19 PM Β· Difficulty 10.9948 Β· 3,517,712 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
db4d979eac0b4e2e6e563a66491620ad849186f4cf1340c65b039b2fb8ac35f2
View on Chainz β†—

Difficulty

10.994809

Transactions

1

Size

200 B

Version

2

Bits

0afeabca

Nonce

566,007,756

Timestamp

7/27/2019, 5:13:19 PM

Confirmations

3,517,712

Merkle Root

45ab9781918e60ff23963db7027009b062532691d05e48391d788b09638b1f06
Transactions (1)
Coinbase45ab9781918e60…788b09638b1f06
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.

3.730 Γ— 10⁹⁴(95-digit number)
37301078068894155328…74899982265815255040
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
3.730 Γ— 10⁹⁴(95-digit number)
37301078068894155328…74899982265815255039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.460 Γ— 10⁹⁴(95-digit number)
74602156137788310657…49799964531630510079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.492 Γ— 10⁹⁡(96-digit number)
14920431227557662131…99599929063261020159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.984 Γ— 10⁹⁡(96-digit number)
29840862455115324262…99199858126522040319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.968 Γ— 10⁹⁡(96-digit number)
59681724910230648525…98399716253044080639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.193 Γ— 10⁹⁢(97-digit number)
11936344982046129705…96799432506088161279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.387 Γ— 10⁹⁢(97-digit number)
23872689964092259410…93598865012176322559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.774 Γ— 10⁹⁢(97-digit number)
47745379928184518820…87197730024352645119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.549 Γ— 10⁹⁢(97-digit number)
95490759856369037641…74395460048705290239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.909 Γ— 10⁹⁷(98-digit number)
19098151971273807528…48790920097410580479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.819 Γ— 10⁹⁷(98-digit number)
38196303942547615056…97581840194821160959
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 3284073

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 db4d979eac0b4e2e6e563a66491620ad849186f4cf1340c65b039b2fb8ac35f2

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 #3,284,073 on Chainz β†—
Circulating Supply:57,658,368 XPMΒ·at block #6,801,784 Β· updates every 60s
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