XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,887,120

Block #2,887,120

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/19/2018, 1:25:01 AM Β· Difficulty 11.6209 Β· 3,945,690 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
699b41df099eeb8d7b1d8ff2f0a2a82a419ed6de05ce772f4d345e9cfeb02e83
View on Chainz β†—

Difficulty

11.620869

Transactions

1

Size

200 B

Version

2

Bits

0b9ef140

Nonce

1,939,798,065

Timestamp

10/19/2018, 1:25:01 AM

Confirmations

3,945,690

Merkle Root

0837e597591f7ddd25bf822f8862524239615079f14250e1232e0968da2dbc61
Transactions (1)
Coinbase0837e597591f7d…2e0968da2dbc61
1 in β†’ 1 out7.3900 XPM110 B
ARy86gMc…MTbANXRz
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.

2.575 Γ— 10⁹³(94-digit number)
25752941926239480254…31877476424842700200
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.575 Γ— 10⁹³(94-digit number)
25752941926239480254…31877476424842700201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.150 Γ— 10⁹³(94-digit number)
51505883852478960509…63754952849685400401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.030 Γ— 10⁹⁴(95-digit number)
10301176770495792101…27509905699370800801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.060 Γ— 10⁹⁴(95-digit number)
20602353540991584203…55019811398741601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.120 Γ— 10⁹⁴(95-digit number)
41204707081983168407…10039622797483203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.240 Γ— 10⁹⁴(95-digit number)
82409414163966336815…20079245594966406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.648 Γ— 10⁹⁡(96-digit number)
16481882832793267363…40158491189932812801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.296 Γ— 10⁹⁡(96-digit number)
32963765665586534726…80316982379865625601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.592 Γ— 10⁹⁡(96-digit number)
65927531331173069452…60633964759731251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.318 Γ— 10⁹⁢(97-digit number)
13185506266234613890…21267929519462502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.637 Γ— 10⁹⁢(97-digit number)
26371012532469227780…42535859038925004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
5.274 Γ— 10⁹⁢(97-digit number)
52742025064938455561…85071718077850009601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second 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
ExceptionalChain length 12
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2887120

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 699b41df099eeb8d7b1d8ff2f0a2a82a419ed6de05ce772f4d345e9cfeb02e83

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 #2,887,120 on Chainz β†—
Circulating Supply:57,906,650 XPMΒ·at block #6,832,809 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