XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,821,555

Block #2,821,555

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/2/2018, 3:31:53 PM Β· Difficulty 11.7030 Β· 4,015,439 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
92c06b8db8dca3063c23ee88977f96ec27ffefe95a0e0f217cfde13a20c3b264
View on Chainz β†—

Difficulty

11.702999

Transactions

1

Size

200 B

Version

2

Bits

0bb3f7c6

Nonce

289,521,697

Timestamp

9/2/2018, 3:31:53 PM

Confirmations

4,015,439

Merkle Root

ce2f3325d69d038203b0f5481c3960f5fe1ebbecdcdccd9580d350b01876bc9f
Transactions (1)
Coinbasece2f3325d69d03…d350b01876bc9f
1 in β†’ 1 out7.2900 XPM110 B
AasD5oKm…HsRC4ypz
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.

3.552 Γ— 10⁹³(94-digit number)
35520078598446344501…18071953616507140960
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
3.552 Γ— 10⁹³(94-digit number)
35520078598446344501…18071953616507140959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.104 Γ— 10⁹³(94-digit number)
71040157196892689002…36143907233014281919
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)
14208031439378537800…72287814466028563839
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)
28416062878757075601…44575628932057127679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.683 Γ— 10⁹⁴(95-digit number)
56832125757514151202…89151257864114255359
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)
11366425151502830240…78302515728228510719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.273 Γ— 10⁹⁡(96-digit number)
22732850303005660480…56605031456457021439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.546 Γ— 10⁹⁡(96-digit number)
45465700606011320961…13210062912914042879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.093 Γ— 10⁹⁡(96-digit number)
90931401212022641923…26420125825828085759
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)
18186280242404528384…52840251651656171519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.637 Γ— 10⁹⁢(97-digit number)
36372560484809056769…05680503303312343039
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 2821555

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 92c06b8db8dca3063c23ee88977f96ec27ffefe95a0e0f217cfde13a20c3b264

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 #2,821,555 on Chainz β†—
Circulating Supply:57,940,253 XPMΒ·at block #6,836,993 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