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Home/Chain Registry/Block #2,630,684

Block #2,630,684

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/26/2018, 2:28:23 PM Β· Difficulty 11.1757 Β· 4,213,913 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4096dff14e9bcc41d716e7505d2dd0eef24b4bbf1fa6e9b5a2e0ad37e055846a
View on Chainz β†—

Difficulty

11.175725

Transactions

1

Size

201 B

Version

2

Bits

0b2cfc50

Nonce

1,415,738,976

Timestamp

4/26/2018, 2:28:23 PM

Confirmations

4,213,913

Merkle Root

243b8b242e600e96493621b5e68292a38a606f157f26b53e305cebba54c3c077
Transactions (1)
Coinbase243b8b242e600e…5cebba54c3c077
1 in β†’ 1 out7.9900 XPM110 B
APtNskS1…p9Z16per
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.

3.941 Γ— 10⁹⁢(97-digit number)
39418735249998039551…99490849170837573760
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
3.941 Γ— 10⁹⁢(97-digit number)
39418735249998039551…99490849170837573759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.883 Γ— 10⁹⁢(97-digit number)
78837470499996079102…98981698341675147519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.576 Γ— 10⁹⁷(98-digit number)
15767494099999215820…97963396683350295039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.153 Γ— 10⁹⁷(98-digit number)
31534988199998431641…95926793366700590079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.306 Γ— 10⁹⁷(98-digit number)
63069976399996863282…91853586733401180159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.261 Γ— 10⁹⁸(99-digit number)
12613995279999372656…83707173466802360319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.522 Γ— 10⁹⁸(99-digit number)
25227990559998745312…67414346933604720639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.045 Γ— 10⁹⁸(99-digit number)
50455981119997490625…34828693867209441279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.009 Γ— 10⁹⁹(100-digit number)
10091196223999498125…69657387734418882559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.018 Γ— 10⁹⁹(100-digit number)
20182392447998996250…39314775468837765119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.036 Γ— 10⁹⁹(100-digit number)
40364784895997992500…78629550937675530239
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 2630684

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 4096dff14e9bcc41d716e7505d2dd0eef24b4bbf1fa6e9b5a2e0ad37e055846a

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 #2,630,684 on Chainz β†—
Circulating Supply:58,001,185 XPMΒ·at block #6,844,596 Β· updates every 60s
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