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Home/Chain Registry/Block #2,833,747

Block #2,833,747

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 11:06:03 PM Β· Difficulty 11.7160 Β· 3,997,842 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
eff9ccbb1083af7cfd8cc647f71fc8649bff9c55788b02525a4100607d6d76d1
View on Chainz β†—

Difficulty

11.716049

Transactions

1

Size

200 B

Version

2

Bits

0bb74ef9

Nonce

1,482,709,814

Timestamp

9/10/2018, 11:06:03 PM

Confirmations

3,997,842

Merkle Root

b65f601b263a8847a8e153bc694efdd47a9991d51d7d1104f815bca7b4e4898b
Transactions (1)
Coinbaseb65f601b263a88…15bca7b4e4898b
1 in β†’ 1 out7.2700 XPM110 B
AHqBB3fe…BpfqTyft
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.

3.041 Γ— 10⁹⁴(95-digit number)
30414084689988223390…31935328719955301280
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
3.041 Γ— 10⁹⁴(95-digit number)
30414084689988223390…31935328719955301279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.082 Γ— 10⁹⁴(95-digit number)
60828169379976446780…63870657439910602559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.216 Γ— 10⁹⁡(96-digit number)
12165633875995289356…27741314879821205119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.433 Γ— 10⁹⁡(96-digit number)
24331267751990578712…55482629759642410239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.866 Γ— 10⁹⁡(96-digit number)
48662535503981157424…10965259519284820479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.732 Γ— 10⁹⁡(96-digit number)
97325071007962314849…21930519038569640959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.946 Γ— 10⁹⁢(97-digit number)
19465014201592462969…43861038077139281919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.893 Γ— 10⁹⁢(97-digit number)
38930028403184925939…87722076154278563839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.786 Γ— 10⁹⁢(97-digit number)
77860056806369851879…75444152308557127679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.557 Γ— 10⁹⁷(98-digit number)
15572011361273970375…50888304617114255359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.114 Γ— 10⁹⁷(98-digit number)
31144022722547940751…01776609234228510719
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 2833747

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 eff9ccbb1083af7cfd8cc647f71fc8649bff9c55788b02525a4100607d6d76d1

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 #2,833,747 on Chainz β†—
Circulating Supply:57,896,809 XPMΒ·at block #6,831,588 Β· updates every 60s
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