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Home/Chain Registry/Block #2,872,010

Block #2,872,010

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 10/8/2018, 2:37:34 AM Β· Difficulty 11.6667 Β· 3,970,924 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a5ad9d29bdd65f1daba0f40c64046d9ea389c814d86e5b27ffe403859d4d116a
View on Chainz β†—

Difficulty

11.666704

Transactions

1

Size

200 B

Version

2

Bits

0baaad16

Nonce

484,080,637

Timestamp

10/8/2018, 2:37:34 AM

Confirmations

3,970,924

Merkle Root

7e365ff03d41d9bc9da088a787c98de44c16764579a5b2b8bacca9af09e8a73a
Transactions (1)
Coinbase7e365ff03d41d9…cca9af09e8a73a
1 in β†’ 1 out7.3300 XPM110 B
AZkoyrUu…aJSS5Bio
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.

1.863 Γ— 10⁹⁡(96-digit number)
18635957934168571520…11868324387714139600
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
1.863 Γ— 10⁹⁡(96-digit number)
18635957934168571520…11868324387714139599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.727 Γ— 10⁹⁡(96-digit number)
37271915868337143041…23736648775428279199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.454 Γ— 10⁹⁡(96-digit number)
74543831736674286082…47473297550856558399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.490 Γ— 10⁹⁢(97-digit number)
14908766347334857216…94946595101713116799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.981 Γ— 10⁹⁢(97-digit number)
29817532694669714433…89893190203426233599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.963 Γ— 10⁹⁢(97-digit number)
59635065389339428866…79786380406852467199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.192 Γ— 10⁹⁷(98-digit number)
11927013077867885773…59572760813704934399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.385 Γ— 10⁹⁷(98-digit number)
23854026155735771546…19145521627409868799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.770 Γ— 10⁹⁷(98-digit number)
47708052311471543092…38291043254819737599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.541 Γ— 10⁹⁷(98-digit number)
95416104622943086185…76582086509639475199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.908 Γ— 10⁹⁸(99-digit number)
19083220924588617237…53164173019278950399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
3.816 Γ— 10⁹⁸(99-digit number)
38166441849177234474…06328346038557900799
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 2872010

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 a5ad9d29bdd65f1daba0f40c64046d9ea389c814d86e5b27ffe403859d4d116a

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 #2,872,010 on Chainz β†—
Circulating Supply:57,987,821 XPMΒ·at block #6,842,933 Β· updates every 60s
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