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Home/Chain Registry/Block #3,049,595

Block #3,049,595

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/12/2019, 9:52:13 AM Β· Difficulty 10.9961 Β· 3,794,489 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8a42b496a0c7375bb5aaef648fb88d2a395dbe8e230afc97efec633edbb967f6
View on Chainz β†—

Difficulty

10.996090

Transactions

1

Size

200 B

Version

2

Bits

0afeffb9

Nonce

1,275,356,893

Timestamp

2/12/2019, 9:52:13 AM

Confirmations

3,794,489

Merkle Root

1ac0c5c5f4c83cabde82169635e3f9be4b665f4a75a275d70fdfc1439fd54569
Transactions (1)
Coinbase1ac0c5c5f4c83c…dfc1439fd54569
1 in β†’ 1 out8.2600 XPM110 B
AbXwmGxD…4XXYP765
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.

2.722 Γ— 10⁹⁡(96-digit number)
27223780672080557588…94590344853163301120
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
2.722 Γ— 10⁹⁡(96-digit number)
27223780672080557588…94590344853163301119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.444 Γ— 10⁹⁡(96-digit number)
54447561344161115177…89180689706326602239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.088 Γ— 10⁹⁢(97-digit number)
10889512268832223035…78361379412653204479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.177 Γ— 10⁹⁢(97-digit number)
21779024537664446071…56722758825306408959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.355 Γ— 10⁹⁢(97-digit number)
43558049075328892142…13445517650612817919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.711 Γ— 10⁹⁢(97-digit number)
87116098150657784284…26891035301225635839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.742 Γ— 10⁹⁷(98-digit number)
17423219630131556856…53782070602451271679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.484 Γ— 10⁹⁷(98-digit number)
34846439260263113713…07564141204902543359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.969 Γ— 10⁹⁷(98-digit number)
69692878520526227427…15128282409805086719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.393 Γ— 10⁹⁸(99-digit number)
13938575704105245485…30256564819610173439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.787 Γ— 10⁹⁸(99-digit number)
27877151408210490971…60513129639220346879
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 3049595

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 8a42b496a0c7375bb5aaef648fb88d2a395dbe8e230afc97efec633edbb967f6

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 #3,049,595 on Chainz β†—
Circulating Supply:57,997,044 XPMΒ·at block #6,844,083 Β· updates every 60s
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