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Block #2,792,361

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/13/2018, 4:15:23 PM Β· Difficulty 11.6751 Β· 4,047,783 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cf91160e4e4e659f223bf06289fcd9a82001f19d54415fd801493de3a6b13cd5
View on Chainz β†—

Difficulty

11.675103

Transactions

1

Size

201 B

Version

2

Bits

0bacd38e

Nonce

1,099,493,899

Timestamp

8/13/2018, 4:15:23 PM

Confirmations

4,047,783

Merkle Root

42d716b6598a8b45041150c81d329b23f3f0dedfd19c1a8ae5b8dbfa643078af
Transactions (1)
Coinbase42d716b6598a8b…b8dbfa643078af
1 in β†’ 1 out7.3200 XPM110 B
ALCTQgeJ…R9C1WZno
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.

1.480 Γ— 10⁹⁢(97-digit number)
14804479472352004454…06323303986182722560
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
1.480 Γ— 10⁹⁢(97-digit number)
14804479472352004454…06323303986182722559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.960 Γ— 10⁹⁢(97-digit number)
29608958944704008909…12646607972365445119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.921 Γ— 10⁹⁢(97-digit number)
59217917889408017819…25293215944730890239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.184 Γ— 10⁹⁷(98-digit number)
11843583577881603563…50586431889461780479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.368 Γ— 10⁹⁷(98-digit number)
23687167155763207127…01172863778923560959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.737 Γ— 10⁹⁷(98-digit number)
47374334311526414255…02345727557847121919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.474 Γ— 10⁹⁷(98-digit number)
94748668623052828511…04691455115694243839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.894 Γ— 10⁹⁸(99-digit number)
18949733724610565702…09382910231388487679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.789 Γ— 10⁹⁸(99-digit number)
37899467449221131404…18765820462776975359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.579 Γ— 10⁹⁸(99-digit number)
75798934898442262809…37531640925553950719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.515 Γ— 10⁹⁹(100-digit number)
15159786979688452561…75063281851107901439
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 2792361

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 cf91160e4e4e659f223bf06289fcd9a82001f19d54415fd801493de3a6b13cd5

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 #2,792,361 on Chainz β†—
Circulating Supply:57,965,469 XPMΒ·at block #6,840,143 Β· updates every 60s
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