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Block #2,825,485

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2018, 7:10:49 AM Β· Difficulty 11.7096 Β· 4,013,792 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7e5fb1adcf6c3041ed48349444d0b4e5232e8f82d722ff2fe6d48d5b6f829ea6
View on Chainz β†—

Difficulty

11.709596

Transactions

1

Size

200 B

Version

2

Bits

0bb5a81a

Nonce

1,096,472,630

Timestamp

9/5/2018, 7:10:49 AM

Confirmations

4,013,792

Merkle Root

90b842ef6ae83e0d5bf208a53fe7fcc2b49d869f9d254958fc9d183224b1ba0f
Transactions (1)
Coinbase90b842ef6ae83e…9d183224b1ba0f
1 in β†’ 1 out7.2800 XPM110 B
AZtxQr2F…7grUWrUz
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.

5.798 Γ— 10⁹⁴(95-digit number)
57981777655064242292…44903968599659333410
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
5.798 Γ— 10⁹⁴(95-digit number)
57981777655064242292…44903968599659333409
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.159 Γ— 10⁹⁡(96-digit number)
11596355531012848458…89807937199318666819
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.319 Γ— 10⁹⁡(96-digit number)
23192711062025696917…79615874398637333639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.638 Γ— 10⁹⁡(96-digit number)
46385422124051393834…59231748797274667279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.277 Γ— 10⁹⁡(96-digit number)
92770844248102787668…18463497594549334559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.855 Γ— 10⁹⁢(97-digit number)
18554168849620557533…36926995189098669119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.710 Γ— 10⁹⁢(97-digit number)
37108337699241115067…73853990378197338239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.421 Γ— 10⁹⁢(97-digit number)
74216675398482230134…47707980756394676479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.484 Γ— 10⁹⁷(98-digit number)
14843335079696446026…95415961512789352959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.968 Γ— 10⁹⁷(98-digit number)
29686670159392892053…90831923025578705919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.937 Γ— 10⁹⁷(98-digit number)
59373340318785784107…81663846051157411839
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 2825485

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 7e5fb1adcf6c3041ed48349444d0b4e5232e8f82d722ff2fe6d48d5b6f829ea6

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 #2,825,485 on Chainz β†—
Circulating Supply:57,958,501 XPMΒ·at block #6,839,276 Β· updates every 60s
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