XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,877,970

Block #2,877,970

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2018, 11:03:58 AM Β· Difficulty 11.6461 Β· 3,967,025 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
91910889675893aa7c6a04162b277a5ef5b6d7dd84b65eab856a4dccd21e97ba
View on Chainz β†—

Difficulty

11.646136

Transactions

1

Size

200 B

Version

2

Bits

0ba5692e

Nonce

1,866,769,507

Timestamp

10/12/2018, 11:03:58 AM

Confirmations

3,967,025

Merkle Root

df9e0a909550ffa05e19845efc8f82b3c1dd031b28ab7b973c45ce8a1a235f2d
Transactions (1)
Coinbasedf9e0a909550ff…45ce8a1a235f2d
1 in β†’ 1 out7.3600 XPM110 B
Acrs2fK9…waGZpPx3
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.

1.659 Γ— 10⁹⁡(96-digit number)
16594075608651456984…71755898323005440000
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
1.659 Γ— 10⁹⁡(96-digit number)
16594075608651456984…71755898323005440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.318 Γ— 10⁹⁡(96-digit number)
33188151217302913968…43511796646010880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.637 Γ— 10⁹⁡(96-digit number)
66376302434605827936…87023593292021760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.327 Γ— 10⁹⁢(97-digit number)
13275260486921165587…74047186584043520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.655 Γ— 10⁹⁢(97-digit number)
26550520973842331174…48094373168087040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.310 Γ— 10⁹⁢(97-digit number)
53101041947684662349…96188746336174080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.062 Γ— 10⁹⁷(98-digit number)
10620208389536932469…92377492672348160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.124 Γ— 10⁹⁷(98-digit number)
21240416779073864939…84754985344696320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.248 Γ— 10⁹⁷(98-digit number)
42480833558147729879…69509970689392640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.496 Γ— 10⁹⁷(98-digit number)
84961667116295459758…39019941378785280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.699 Γ— 10⁹⁸(99-digit number)
16992333423259091951…78039882757570560001
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 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
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 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 2877970

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 91910889675893aa7c6a04162b277a5ef5b6d7dd84b65eab856a4dccd21e97ba

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 #2,877,970 on Chainz β†—
Circulating Supply:58,004,381 XPMΒ·at block #6,844,994 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