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Home/Chain Registry/Block #2,800,700

Block #2,800,700

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/19/2018, 12:13:56 PM Β· Difficulty 11.6715 Β· 4,044,950 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
310da52159d0280bf42c4c6cb02e16bed822ae7ad900b17186927bfed57bbb85
View on Chainz β†—

Difficulty

11.671488

Transactions

2

Size

574 B

Version

2

Bits

0babe6a9

Nonce

1,636,195,806

Timestamp

8/19/2018, 12:13:56 PM

Confirmations

4,044,950

Merkle Root

03a5a42068476d641475cf913f01dfada9bcecf7f8bbbe414bce967e7ee6c76c
Transactions (2)
Coinbaseb01ef4969a584b…f1b81e98ae05e4
1 in β†’ 1 out7.3400 XPM110 B
AG3T4UpC…1EXu2o4b
753228da3863ca…e708e1520d32e2
2 in β†’ 2 out5.9600 XPM374 B
AZi9mugB…1meALKxUAbbpasAS…u5puw5AA
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.

5.073 Γ— 10⁹³(94-digit number)
50732370862672375875…65176395493013997390
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
5.073 Γ— 10⁹³(94-digit number)
50732370862672375875…65176395493013997389
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.014 Γ— 10⁹⁴(95-digit number)
10146474172534475175…30352790986027994779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.029 Γ— 10⁹⁴(95-digit number)
20292948345068950350…60705581972055989559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.058 Γ— 10⁹⁴(95-digit number)
40585896690137900700…21411163944111979119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.117 Γ— 10⁹⁴(95-digit number)
81171793380275801401…42822327888223958239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.623 Γ— 10⁹⁡(96-digit number)
16234358676055160280…85644655776447916479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.246 Γ— 10⁹⁡(96-digit number)
32468717352110320560…71289311552895832959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.493 Γ— 10⁹⁡(96-digit number)
64937434704220641120…42578623105791665919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.298 Γ— 10⁹⁢(97-digit number)
12987486940844128224…85157246211583331839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.597 Γ— 10⁹⁢(97-digit number)
25974973881688256448…70314492423166663679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.194 Γ— 10⁹⁢(97-digit number)
51949947763376512896…40628984846333327359
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 2800700

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 310da52159d0280bf42c4c6cb02e16bed822ae7ad900b17186927bfed57bbb85

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 #2,800,700 on Chainz β†—
Circulating Supply:58,009,649 XPMΒ·at block #6,845,649 Β· updates every 60s
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