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Block #2,817,770

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/31/2018, 2:27:30 AM Β· Difficulty 11.6957 Β· 4,023,153 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
68e0587df1a0218d22d9c6937a456e856a4bdb3bebdc154541bd7fbc6681a827
View on Chainz β†—

Difficulty

11.695710

Transactions

1

Size

200 B

Version

2

Bits

0bb21a15

Nonce

610,357,558

Timestamp

8/31/2018, 2:27:30 AM

Confirmations

4,023,153

Merkle Root

5dc786ebb554072e023e41023c2499d5346d2cd13b33c345c3e000353305c5a5
Transactions (1)
Coinbase5dc786ebb55407…e000353305c5a5
1 in β†’ 1 out7.3000 XPM110 B
AP4v1gaq…dwWVhP9P
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.

8.706 Γ— 10⁹⁡(96-digit number)
87063285281575432802…84237226860582721280
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
8.706 Γ— 10⁹⁡(96-digit number)
87063285281575432802…84237226860582721279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.741 Γ— 10⁹⁢(97-digit number)
17412657056315086560…68474453721165442559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.482 Γ— 10⁹⁢(97-digit number)
34825314112630173121…36948907442330885119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.965 Γ— 10⁹⁢(97-digit number)
69650628225260346242…73897814884661770239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.393 Γ— 10⁹⁷(98-digit number)
13930125645052069248…47795629769323540479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.786 Γ— 10⁹⁷(98-digit number)
27860251290104138496…95591259538647080959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.572 Γ— 10⁹⁷(98-digit number)
55720502580208276993…91182519077294161919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.114 Γ— 10⁹⁸(99-digit number)
11144100516041655398…82365038154588323839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.228 Γ— 10⁹⁸(99-digit number)
22288201032083310797…64730076309176647679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.457 Γ— 10⁹⁸(99-digit number)
44576402064166621595…29460152618353295359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.915 Γ— 10⁹⁸(99-digit number)
89152804128333243190…58920305236706590719
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 2817770

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 68e0587df1a0218d22d9c6937a456e856a4bdb3bebdc154541bd7fbc6681a827

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 #2,817,770 on Chainz β†—
Circulating Supply:57,971,736 XPMΒ·at block #6,840,922 Β· updates every 60s
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