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Home/Chain Registry/Block #2,807,210

Block #2,807,210

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/24/2018, 12:11:50 AM Β· Difficulty 11.6738 Β· 4,037,482 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0356f29283d38808f2aef6a6bb702a4639f85bee11b8c5ba5d22b1d07fc13067
View on Chainz β†—

Difficulty

11.673798

Transactions

1

Size

200 B

Version

2

Bits

0bac7e07

Nonce

673,997,441

Timestamp

8/24/2018, 12:11:50 AM

Confirmations

4,037,482

Merkle Root

58e568256a6bd11db9fa21de576c83b755898ed3dac5c1e3cdddc2104e5be5f9
Transactions (1)
Coinbase58e568256a6bd1…ddc2104e5be5f9
1 in β†’ 1 out7.3300 XPM110 B
AUJZraeJ…xyGgCHtV
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.

4.500 Γ— 10⁹⁡(96-digit number)
45009202163764440641…76307250809341934080
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
4.500 Γ— 10⁹⁡(96-digit number)
45009202163764440641…76307250809341934079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.001 Γ— 10⁹⁡(96-digit number)
90018404327528881283…52614501618683868159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.800 Γ— 10⁹⁢(97-digit number)
18003680865505776256…05229003237367736319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.600 Γ— 10⁹⁢(97-digit number)
36007361731011552513…10458006474735472639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.201 Γ— 10⁹⁢(97-digit number)
72014723462023105026…20916012949470945279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.440 Γ— 10⁹⁷(98-digit number)
14402944692404621005…41832025898941890559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.880 Γ— 10⁹⁷(98-digit number)
28805889384809242010…83664051797883781119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.761 Γ— 10⁹⁷(98-digit number)
57611778769618484021…67328103595767562239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.152 Γ— 10⁹⁸(99-digit number)
11522355753923696804…34656207191535124479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.304 Γ— 10⁹⁸(99-digit number)
23044711507847393608…69312414383070248959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.608 Γ— 10⁹⁸(99-digit number)
46089423015694787217…38624828766140497919
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 2807210

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 0356f29283d38808f2aef6a6bb702a4639f85bee11b8c5ba5d22b1d07fc13067

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 #2,807,210 on Chainz β†—
Circulating Supply:58,001,944 XPMΒ·at block #6,844,691 Β· updates every 60s
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