XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,657,289

Block #2,657,289

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/11/2018, 8:41:17 PM Β· Difficulty 11.6721 Β· 4,184,960 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4283edbd1ca7533750a72b3f2e657cfbcd5428361e004d5f8350988fe0d1b75e
View on Chainz β†—

Difficulty

11.672084

Transactions

1

Size

201 B

Version

2

Bits

0bac0dba

Nonce

1,113,079,190

Timestamp

5/11/2018, 8:41:17 PM

Confirmations

4,184,960

Merkle Root

35df9e53c8e6547f5f3581fafa902a64eb7bdc4f51e7942f10058be7f8f3d87f
Transactions (1)
Coinbase35df9e53c8e654…058be7f8f3d87f
1 in β†’ 1 out7.3300 XPM110 B
AeMAzDss…DADyueAD
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.

5.064 Γ— 10⁹⁢(97-digit number)
50644855878396434567…76542125052919234560
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.064 Γ— 10⁹⁢(97-digit number)
50644855878396434567…76542125052919234559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.012 Γ— 10⁹⁷(98-digit number)
10128971175679286913…53084250105838469119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.025 Γ— 10⁹⁷(98-digit number)
20257942351358573827…06168500211676938239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.051 Γ— 10⁹⁷(98-digit number)
40515884702717147654…12337000423353876479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.103 Γ— 10⁹⁷(98-digit number)
81031769405434295308…24674000846707752959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.620 Γ— 10⁹⁸(99-digit number)
16206353881086859061…49348001693415505919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.241 Γ— 10⁹⁸(99-digit number)
32412707762173718123…98696003386831011839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.482 Γ— 10⁹⁸(99-digit number)
64825415524347436246…97392006773662023679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.296 Γ— 10⁹⁹(100-digit number)
12965083104869487249…94784013547324047359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.593 Γ— 10⁹⁹(100-digit number)
25930166209738974498…89568027094648094719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.186 Γ— 10⁹⁹(100-digit number)
51860332419477948997…79136054189296189439
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2657289

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 4283edbd1ca7533750a72b3f2e657cfbcd5428361e004d5f8350988fe0d1b75e

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 #2,657,289 on Chainz β†—
Circulating Supply:57,982,390 XPMΒ·at block #6,842,248 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