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Home/Chain Registry/Block #2,683,120

Block #2,683,120

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/29/2018, 2:44:18 PM Β· Difficulty 11.6899 Β· 4,159,909 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
784ed2ac36c8f6c308b0f392488c262a55e3ece423cf63a6b02ab863875776aa
View on Chainz β†—

Difficulty

11.689895

Transactions

1

Size

201 B

Version

2

Bits

0bb09cf4

Nonce

753,899,755

Timestamp

5/29/2018, 2:44:18 PM

Confirmations

4,159,909

Merkle Root

f8df1b8fbb6068e943c12036b74426114204ceadcfb1b45e1a6fec520c30b0bb
Transactions (1)
Coinbasef8df1b8fbb6068…6fec520c30b0bb
1 in β†’ 1 out7.3100 XPM110 B
ALh1kAmi…8BASXF21
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.

2.976 Γ— 10⁹⁢(97-digit number)
29764529032551743727…10822475775641835520
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
2.976 Γ— 10⁹⁢(97-digit number)
29764529032551743727…10822475775641835519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.952 Γ— 10⁹⁢(97-digit number)
59529058065103487454…21644951551283671039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.190 Γ— 10⁹⁷(98-digit number)
11905811613020697490…43289903102567342079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.381 Γ— 10⁹⁷(98-digit number)
23811623226041394981…86579806205134684159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.762 Γ— 10⁹⁷(98-digit number)
47623246452082789963…73159612410269368319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.524 Γ— 10⁹⁷(98-digit number)
95246492904165579927…46319224820538736639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.904 Γ— 10⁹⁸(99-digit number)
19049298580833115985…92638449641077473279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.809 Γ— 10⁹⁸(99-digit number)
38098597161666231970…85276899282154946559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.619 Γ— 10⁹⁸(99-digit number)
76197194323332463941…70553798564309893119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.523 Γ— 10⁹⁹(100-digit number)
15239438864666492788…41107597128619786239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.047 Γ— 10⁹⁹(100-digit number)
30478877729332985576…82215194257239572479
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 2683120

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 784ed2ac36c8f6c308b0f392488c262a55e3ece423cf63a6b02ab863875776aa

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 #2,683,120 on Chainz β†—
Circulating Supply:57,988,586 XPMΒ·at block #6,843,028 Β· updates every 60s
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