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Home/Chain Registry/Block #2,592,069

Block #2,592,069

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/30/2018, 2:31:03 AM Β· Difficulty 11.3203 Β· 4,234,732 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1361d34e16ff13f479cfe2d98e131dd5259cd33413073801a6f8ed93fd4d0c6c
View on Chainz β†—

Difficulty

11.320274

Transactions

1

Size

200 B

Version

2

Bits

0b51fd80

Nonce

1,768,004,271

Timestamp

3/30/2018, 2:31:03 AM

Confirmations

4,234,732

Merkle Root

91b3d0c7d55227570f1e6936bf575c01c1672ac220be0f6b7898c5e494534cb3
Transactions (1)
Coinbase91b3d0c7d55227…98c5e494534cb3
1 in β†’ 1 out7.7900 XPM110 B
AVZttTmX…wg6mbABB
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.

1.246 Γ— 10⁹⁡(96-digit number)
12466830858456071983…94552035140595554560
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
1.246 Γ— 10⁹⁡(96-digit number)
12466830858456071983…94552035140595554559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.493 Γ— 10⁹⁡(96-digit number)
24933661716912143966…89104070281191109119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.986 Γ— 10⁹⁡(96-digit number)
49867323433824287933…78208140562382218239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.973 Γ— 10⁹⁡(96-digit number)
99734646867648575867…56416281124764436479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.994 Γ— 10⁹⁢(97-digit number)
19946929373529715173…12832562249528872959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.989 Γ— 10⁹⁢(97-digit number)
39893858747059430346…25665124499057745919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.978 Γ— 10⁹⁢(97-digit number)
79787717494118860693…51330248998115491839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.595 Γ— 10⁹⁷(98-digit number)
15957543498823772138…02660497996230983679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.191 Γ— 10⁹⁷(98-digit number)
31915086997647544277…05320995992461967359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.383 Γ— 10⁹⁷(98-digit number)
63830173995295088554…10641991984923934719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.276 Γ— 10⁹⁸(99-digit number)
12766034799059017710…21283983969847869439
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 2592069

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 1361d34e16ff13f479cfe2d98e131dd5259cd33413073801a6f8ed93fd4d0c6c

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 #2,592,069 on Chainz β†—
Circulating Supply:57,858,571 XPMΒ·at block #6,826,800 Β· updates every 60s
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