XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,237,320

Block #2,237,320

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/5/2017, 12:40:10 AM Β· Difficulty 10.9460 Β· 4,606,739 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2437cf8b41c195140f0e80e84e090f1175ff6feadb895410a7858a507b3689b8
View on Chainz β†—

Difficulty

10.946009

Transactions

2

Size

1015 B

Version

2

Bits

0af22da0

Nonce

926,080,173

Timestamp

8/5/2017, 12:40:10 AM

Confirmations

4,606,739

Merkle Root

839f438b870e2dfea74cf690b87c5f6b447a9cf1c75b7ca97f3e27af1f4d35c0
Transactions (2)
Coinbasebb854008c42a86…abfc78805e74eb
1 in β†’ 1 out8.3400 XPM109 B
AWCEsR62…AeXdmTLx
143c02df5d273b…dd5555c8d6d265
5 in β†’ 2 out2970.0113 XPM815 B
Adf1QQAY…qAyAa4HAAesaHg9U…6tjRExna
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.

8.233 Γ— 10⁹⁡(96-digit number)
82338874181913807439…45077889880881452800
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
8.233 Γ— 10⁹⁡(96-digit number)
82338874181913807439…45077889880881452801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.646 Γ— 10⁹⁢(97-digit number)
16467774836382761487…90155779761762905601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.293 Γ— 10⁹⁢(97-digit number)
32935549672765522975…80311559523525811201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.587 Γ— 10⁹⁢(97-digit number)
65871099345531045951…60623119047051622401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.317 Γ— 10⁹⁷(98-digit number)
13174219869106209190…21246238094103244801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.634 Γ— 10⁹⁷(98-digit number)
26348439738212418380…42492476188206489601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.269 Γ— 10⁹⁷(98-digit number)
52696879476424836761…84984952376412979201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.053 Γ— 10⁹⁸(99-digit number)
10539375895284967352…69969904752825958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.107 Γ— 10⁹⁸(99-digit number)
21078751790569934704…39939809505651916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.215 Γ— 10⁹⁸(99-digit number)
42157503581139869409…79879619011303833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.431 Γ— 10⁹⁸(99-digit number)
84315007162279738818…59759238022607667201
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 2237320

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 2437cf8b41c195140f0e80e84e090f1175ff6feadb895410a7858a507b3689b8

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 #2,237,320 on Chainz β†—
Circulating Supply:57,996,844 XPMΒ·at block #6,844,058 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