XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,644,171

Block #2,644,171

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 9:23:16 AM Β· Difficulty 11.7038 Β· 4,198,870 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
81bea471f2047dae805bee1e6f9beabfa2fcafbe5f9ef2495b3e19ddb5188747
View on Chainz β†—

Difficulty

11.703771

Transactions

1

Size

199 B

Version

2

Bits

0bb42a58

Nonce

1,056,545,786

Timestamp

5/2/2018, 9:23:16 AM

Confirmations

4,198,870

Merkle Root

253a3d50cb7ff91ccd51e3f20439c69d4d90d338ca2124919204f0b5a249c7e4
Transactions (1)
Coinbase253a3d50cb7ff9…04f0b5a249c7e4
1 in β†’ 1 out7.2900 XPM110 B
ANxCJWUy…fh9w5iLB
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.

1.697 Γ— 10⁹³(94-digit number)
16970416428097278300…59475338440452074820
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
1.697 Γ— 10⁹³(94-digit number)
16970416428097278300…59475338440452074819
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.394 Γ— 10⁹³(94-digit number)
33940832856194556601…18950676880904149639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.788 Γ— 10⁹³(94-digit number)
67881665712389113202…37901353761808299279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.357 Γ— 10⁹⁴(95-digit number)
13576333142477822640…75802707523616598559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.715 Γ— 10⁹⁴(95-digit number)
27152666284955645281…51605415047233197119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.430 Γ— 10⁹⁴(95-digit number)
54305332569911290562…03210830094466394239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.086 Γ— 10⁹⁡(96-digit number)
10861066513982258112…06421660188932788479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.172 Γ— 10⁹⁡(96-digit number)
21722133027964516224…12843320377865576959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.344 Γ— 10⁹⁡(96-digit number)
43444266055929032449…25686640755731153919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.688 Γ— 10⁹⁡(96-digit number)
86888532111858064899…51373281511462307839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.737 Γ— 10⁹⁢(97-digit number)
17377706422371612979…02746563022924615679
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 2644171

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 81bea471f2047dae805bee1e6f9beabfa2fcafbe5f9ef2495b3e19ddb5188747

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 #2,644,171 on Chainz β†—
Circulating Supply:57,988,685 XPMΒ·at block #6,843,040 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy