XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,762,911

Block #2,762,911

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/24/2018, 10:06:50 AM Β· Difficulty 11.6553 Β· 4,076,960 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cce758eb6dc2a77a478d4f446f877373c488315e21154341981b24e34cc20c2c
View on Chainz β†—

Difficulty

11.655344

Transactions

1

Size

201 B

Version

2

Bits

0ba7c499

Nonce

824,715,607

Timestamp

7/24/2018, 10:06:50 AM

Confirmations

4,076,960

Merkle Root

526ba2494d7354a02cb3c7fba3d09e25ee32f0bf23e6d97263acc868b34a2e43
Transactions (1)
Coinbase526ba2494d7354…acc868b34a2e43
1 in β†’ 1 out7.3500 XPM110 B
ANXKsEDp…mzdusdgP
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.

1.422 Γ— 10⁹⁷(98-digit number)
14224494857783556627…06386313407085578240
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
1.422 Γ— 10⁹⁷(98-digit number)
14224494857783556627…06386313407085578241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.844 Γ— 10⁹⁷(98-digit number)
28448989715567113255…12772626814171156481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.689 Γ— 10⁹⁷(98-digit number)
56897979431134226510…25545253628342312961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.137 Γ— 10⁹⁸(99-digit number)
11379595886226845302…51090507256684625921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.275 Γ— 10⁹⁸(99-digit number)
22759191772453690604…02181014513369251841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.551 Γ— 10⁹⁸(99-digit number)
45518383544907381208…04362029026738503681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.103 Γ— 10⁹⁸(99-digit number)
91036767089814762416…08724058053477007361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.820 Γ— 10⁹⁹(100-digit number)
18207353417962952483…17448116106954014721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.641 Γ— 10⁹⁹(100-digit number)
36414706835925904966…34896232213908029441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.282 Γ— 10⁹⁹(100-digit number)
72829413671851809933…69792464427816058881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.456 Γ— 10¹⁰⁰(101-digit number)
14565882734370361986…39584928855632117761
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 2762911

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 cce758eb6dc2a77a478d4f446f877373c488315e21154341981b24e34cc20c2c

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 #2,762,911 on Chainz β†—
Circulating Supply:57,963,268 XPMΒ·at block #6,839,870 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