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Home/Chain Registry/Block #2,585,652

Block #2,585,652

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/25/2018, 11:05:00 PM Β· Difficulty 11.2564 Β· 4,246,490 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
14e012f7e46cf92770d4dca70326fdf7915e473cbecf3d4942b209e3d8962a5b
View on Chainz β†—

Difficulty

11.256353

Transactions

1

Size

200 B

Version

2

Bits

0b41a052

Nonce

1,503,418,395

Timestamp

3/25/2018, 11:05:00 PM

Confirmations

4,246,490

Merkle Root

5ce4fa21b5bd4c9b89e1255a88b997e4a50cfc4abbd2a8259298571c47534094
Transactions (1)
Coinbase5ce4fa21b5bd4c…98571c47534094
1 in β†’ 1 out7.8800 XPM109 B
Adqah8zh…1WwoHJ9t
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.

6.665 Γ— 10⁹⁡(96-digit number)
66655440594478682933…97871189361890150400
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
6.665 Γ— 10⁹⁡(96-digit number)
66655440594478682933…97871189361890150399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.333 Γ— 10⁹⁢(97-digit number)
13331088118895736586…95742378723780300799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.666 Γ— 10⁹⁢(97-digit number)
26662176237791473173…91484757447560601599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.332 Γ— 10⁹⁢(97-digit number)
53324352475582946346…82969514895121203199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.066 Γ— 10⁹⁷(98-digit number)
10664870495116589269…65939029790242406399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.132 Γ— 10⁹⁷(98-digit number)
21329740990233178538…31878059580484812799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.265 Γ— 10⁹⁷(98-digit number)
42659481980466357077…63756119160969625599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.531 Γ— 10⁹⁷(98-digit number)
85318963960932714154…27512238321939251199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.706 Γ— 10⁹⁸(99-digit number)
17063792792186542830…55024476643878502399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.412 Γ— 10⁹⁸(99-digit number)
34127585584373085661…10048953287757004799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.825 Γ— 10⁹⁸(99-digit number)
68255171168746171323…20097906575514009599
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 2585652

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 14e012f7e46cf92770d4dca70326fdf7915e473cbecf3d4942b209e3d8962a5b

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 #2,585,652 on Chainz β†—
Circulating Supply:57,901,273 XPMΒ·at block #6,832,141 Β· updates every 60s
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