XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,687,370

Block #2,687,370

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/1/2018, 4:03:35 PM Β· Difficulty 11.6807 Β· 4,144,542 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
06199bea92996fcd1f0ee1f4c6fb6160f83da787381e7ba35fb623e75785a813
View on Chainz β†—

Difficulty

11.680727

Transactions

1

Size

200 B

Version

2

Bits

0bae4420

Nonce

2,061,626,204

Timestamp

6/1/2018, 4:03:35 PM

Confirmations

4,144,542

Merkle Root

4bf8595b8bfe53b4b0c409362b599ea2720bf22dcd772e925517404bfdc0bac4
Transactions (1)
Coinbase4bf8595b8bfe53…17404bfdc0bac4
1 in β†’ 1 out7.3200 XPM110 B
Adqah8zh…1WwoHJ9t
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.

6.072 Γ— 10⁹⁡(96-digit number)
60725331115982634124…47072323219771330560
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
6.072 Γ— 10⁹⁡(96-digit number)
60725331115982634124…47072323219771330561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.214 Γ— 10⁹⁢(97-digit number)
12145066223196526824…94144646439542661121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.429 Γ— 10⁹⁢(97-digit number)
24290132446393053649…88289292879085322241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.858 Γ— 10⁹⁢(97-digit number)
48580264892786107299…76578585758170644481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.716 Γ— 10⁹⁢(97-digit number)
97160529785572214599…53157171516341288961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.943 Γ— 10⁹⁷(98-digit number)
19432105957114442919…06314343032682577921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.886 Γ— 10⁹⁷(98-digit number)
38864211914228885839…12628686065365155841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.772 Γ— 10⁹⁷(98-digit number)
77728423828457771679…25257372130730311681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.554 Γ— 10⁹⁸(99-digit number)
15545684765691554335…50514744261460623361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.109 Γ— 10⁹⁸(99-digit number)
31091369531383108671…01029488522921246721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.218 Γ— 10⁹⁸(99-digit number)
62182739062766217343…02058977045842493441
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 2687370

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 06199bea92996fcd1f0ee1f4c6fb6160f83da787381e7ba35fb623e75785a813

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 #2,687,370 on Chainz β†—
Circulating Supply:57,899,420 XPMΒ·at block #6,831,911 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