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Block #2,468,512

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/11/2018, 9:00:54 PM Β· Difficulty 10.9602 Β· 4,375,614 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
971cb8d59c8ddacd5fa5119eb57463a47d300d3e423eef3673ec5e13d8cc35fc
View on Chainz β†—

Difficulty

10.960151

Transactions

1

Size

200 B

Version

2

Bits

0af5cc78

Nonce

802,829,735

Timestamp

1/11/2018, 9:00:54 PM

Confirmations

4,375,614

Merkle Root

b481a8aaab874bf3b0dbc52cfa78037b13897be952b22c8ce0ead90fe2f9a3ac
Transactions (1)
Coinbaseb481a8aaab874b…ead90fe2f9a3ac
1 in β†’ 1 out8.3100 XPM110 B
AJXt95sK…mvkYV89D
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.

4.265 Γ— 10⁹³(94-digit number)
42657735237627543251…09277985646582750000
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
4.265 Γ— 10⁹³(94-digit number)
42657735237627543251…09277985646582749999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.531 Γ— 10⁹³(94-digit number)
85315470475255086502…18555971293165499999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.706 Γ— 10⁹⁴(95-digit number)
17063094095051017300…37111942586330999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.412 Γ— 10⁹⁴(95-digit number)
34126188190102034601…74223885172661999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.825 Γ— 10⁹⁴(95-digit number)
68252376380204069202…48447770345323999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.365 Γ— 10⁹⁡(96-digit number)
13650475276040813840…96895540690647999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.730 Γ— 10⁹⁡(96-digit number)
27300950552081627680…93791081381295999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.460 Γ— 10⁹⁡(96-digit number)
54601901104163255361…87582162762591999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.092 Γ— 10⁹⁢(97-digit number)
10920380220832651072…75164325525183999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.184 Γ— 10⁹⁢(97-digit number)
21840760441665302144…50328651050367999999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2468512

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 971cb8d59c8ddacd5fa5119eb57463a47d300d3e423eef3673ec5e13d8cc35fc

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 #2,468,512 on Chainz β†—
Circulating Supply:57,997,381 XPMΒ·at block #6,844,125 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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