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Block #3,181,558

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/14/2019, 9:13:10 AM Β· Difficulty 11.2588 Β· 3,660,365 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e79686f235c8f2bb199446c614b579bfc0019ad0a4ee203ea0429b707a016b9c
View on Chainz β†—

Difficulty

11.258833

Transactions

1

Size

201 B

Version

2

Bits

0b4242e1

Nonce

893,187,439

Timestamp

5/14/2019, 9:13:10 AM

Confirmations

3,660,365

Merkle Root

bac623572e8f00dbeffee1c090b1bcf97060f4208e07499f35c4a5b3529c9df5
Transactions (1)
Coinbasebac623572e8f00…c4a5b3529c9df5
1 in β†’ 1 out7.8800 XPM110 B
ARbm48qR…9xQc8DBX
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.

1.398 Γ— 10⁹⁷(98-digit number)
13986347882015910080…39871205884392304640
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
1.398 Γ— 10⁹⁷(98-digit number)
13986347882015910080…39871205884392304639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.797 Γ— 10⁹⁷(98-digit number)
27972695764031820160…79742411768784609279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.594 Γ— 10⁹⁷(98-digit number)
55945391528063640320…59484823537569218559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.118 Γ— 10⁹⁸(99-digit number)
11189078305612728064…18969647075138437119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.237 Γ— 10⁹⁸(99-digit number)
22378156611225456128…37939294150276874239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.475 Γ— 10⁹⁸(99-digit number)
44756313222450912256…75878588300553748479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.951 Γ— 10⁹⁸(99-digit number)
89512626444901824512…51757176601107496959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.790 Γ— 10⁹⁹(100-digit number)
17902525288980364902…03514353202214993919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.580 Γ— 10⁹⁹(100-digit number)
35805050577960729804…07028706404429987839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.161 Γ— 10⁹⁹(100-digit number)
71610101155921459609…14057412808859975679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.432 Γ— 10¹⁰⁰(101-digit number)
14322020231184291921…28114825617719951359
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 3181558

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 e79686f235c8f2bb199446c614b579bfc0019ad0a4ee203ea0429b707a016b9c

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 #3,181,558 on Chainz β†—
Circulating Supply:57,979,761 XPMΒ·at block #6,841,922 Β· updates every 60s
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