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Home/Chain Registry/Block #2,683,934

Block #2,683,934

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/30/2018, 4:02:10 AM Β· Difficulty 11.6909 Β· 4,158,603 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c9436a9def936e3d0e6d93eddd932cb76f73ac7d2c4affb110ebe6e3026978bd
View on Chainz β†—

Difficulty

11.690895

Transactions

1

Size

200 B

Version

2

Bits

0bb0de7d

Nonce

173,507,749

Timestamp

5/30/2018, 4:02:10 AM

Confirmations

4,158,603

Merkle Root

8bad7f687e95e6242b0656b1a0f2ad8bca0bbcdc632ccedf4b5e751e1b421937
Transactions (1)
Coinbase8bad7f687e95e6…5e751e1b421937
1 in β†’ 1 out7.3000 XPM110 B
AQnVhM4U…ZbazNfH8
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.

5.735 Γ— 10⁹⁡(96-digit number)
57351194225927551718…88410120943156132400
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
5.735 Γ— 10⁹⁡(96-digit number)
57351194225927551718…88410120943156132399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.147 Γ— 10⁹⁢(97-digit number)
11470238845185510343…76820241886312264799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.294 Γ— 10⁹⁢(97-digit number)
22940477690371020687…53640483772624529599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.588 Γ— 10⁹⁢(97-digit number)
45880955380742041374…07280967545249059199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.176 Γ— 10⁹⁢(97-digit number)
91761910761484082749…14561935090498118399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.835 Γ— 10⁹⁷(98-digit number)
18352382152296816549…29123870180996236799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.670 Γ— 10⁹⁷(98-digit number)
36704764304593633099…58247740361992473599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.340 Γ— 10⁹⁷(98-digit number)
73409528609187266199…16495480723984947199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.468 Γ— 10⁹⁸(99-digit number)
14681905721837453239…32990961447969894399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.936 Γ— 10⁹⁸(99-digit number)
29363811443674906479…65981922895939788799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.872 Γ— 10⁹⁸(99-digit number)
58727622887349812959…31963845791879577599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.174 Γ— 10⁹⁹(100-digit number)
11745524577469962591…63927691583759155199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2683934

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 c9436a9def936e3d0e6d93eddd932cb76f73ac7d2c4affb110ebe6e3026978bd

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 #2,683,934 on Chainz β†—
Circulating Supply:57,984,719 XPMΒ·at block #6,842,536 Β· updates every 60s
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