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Home/Chain Registry/Block #2,648,889

Block #2,648,889

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 8:24:03 PM Β· Difficulty 11.7655 Β· 4,184,887 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8dca00acb3022a8841d8cd6fe4319a12751eddaf51bad678c4ac7c63e6e6f571
View on Chainz β†—

Difficulty

11.765526

Transactions

1

Size

198 B

Version

2

Bits

0bc3f984

Nonce

1,711,626,825

Timestamp

5/4/2018, 8:24:03 PM

Confirmations

4,184,887

Merkle Root

12e906a69f19604ea496cd8608601eee31c428365462e4d31cf27efc79064555
Transactions (1)
Coinbase12e906a69f1960…f27efc79064555
1 in β†’ 1 out7.2100 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.

3.551 Γ— 10⁹³(94-digit number)
35514956946341916596…76271900990801197890
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
3.551 Γ— 10⁹³(94-digit number)
35514956946341916596…76271900990801197889
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.102 Γ— 10⁹³(94-digit number)
71029913892683833192…52543801981602395779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.420 Γ— 10⁹⁴(95-digit number)
14205982778536766638…05087603963204791559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.841 Γ— 10⁹⁴(95-digit number)
28411965557073533276…10175207926409583119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.682 Γ— 10⁹⁴(95-digit number)
56823931114147066553…20350415852819166239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.136 Γ— 10⁹⁡(96-digit number)
11364786222829413310…40700831705638332479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.272 Γ— 10⁹⁡(96-digit number)
22729572445658826621…81401663411276664959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.545 Γ— 10⁹⁡(96-digit number)
45459144891317653243…62803326822553329919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.091 Γ— 10⁹⁡(96-digit number)
90918289782635306486…25606653645106659839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.818 Γ— 10⁹⁢(97-digit number)
18183657956527061297…51213307290213319679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.636 Γ— 10⁹⁢(97-digit number)
36367315913054122594…02426614580426639359
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 2648889

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 8dca00acb3022a8841d8cd6fe4319a12751eddaf51bad678c4ac7c63e6e6f571

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 #2,648,889 on Chainz β†—
Circulating Supply:57,914,426 XPMΒ·at block #6,833,775 Β· updates every 60s
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