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Home/Chain Registry/Block #3,011,738

Block #3,011,738

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/16/2019, 8:18:41 AM Β· Difficulty 11.1759 Β· 3,830,965 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6271c39c171573a1a493b2700622156ab8c314b2bf209c15e8cf3ee8d4b45931
View on Chainz β†—

Difficulty

11.175906

Transactions

1

Size

199 B

Version

2

Bits

0b2d082f

Nonce

663,050,045

Timestamp

1/16/2019, 8:18:41 AM

Confirmations

3,830,965

Merkle Root

1a48d605991777307484cad2b9ddf58b3a838edb12b535580fdc5a1fd642f48a
Transactions (1)
Coinbase1a48d605991777…dc5a1fd642f48a
1 in β†’ 1 out7.9900 XPM110 B
AUhjokok…k5m93PZR
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.

1.390 Γ— 10⁹³(94-digit number)
13909016533368358858…00230364974043875880
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
1.390 Γ— 10⁹³(94-digit number)
13909016533368358858…00230364974043875879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.781 Γ— 10⁹³(94-digit number)
27818033066736717716…00460729948087751759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.563 Γ— 10⁹³(94-digit number)
55636066133473435433…00921459896175503519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.112 Γ— 10⁹⁴(95-digit number)
11127213226694687086…01842919792351007039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.225 Γ— 10⁹⁴(95-digit number)
22254426453389374173…03685839584702014079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.450 Γ— 10⁹⁴(95-digit number)
44508852906778748347…07371679169404028159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.901 Γ— 10⁹⁴(95-digit number)
89017705813557496694…14743358338808056319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.780 Γ— 10⁹⁡(96-digit number)
17803541162711499338…29486716677616112639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.560 Γ— 10⁹⁡(96-digit number)
35607082325422998677…58973433355232225279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.121 Γ— 10⁹⁡(96-digit number)
71214164650845997355…17946866710464450559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.424 Γ— 10⁹⁢(97-digit number)
14242832930169199471…35893733420928901119
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 3011738

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 6271c39c171573a1a493b2700622156ab8c314b2bf209c15e8cf3ee8d4b45931

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 #3,011,738 on Chainz β†—
Circulating Supply:57,985,973 XPMΒ·at block #6,842,702 Β· updates every 60s
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