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Home/Chain Registry/Block #2,649,009

Block #2,649,009

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 10:31:37 PM Β· Difficulty 11.7652 Β· 4,192,961 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
67c213882f2e9193223686afba9ade8e6308dadbbfc6b976fbe6574de1bbf7aa
View on Chainz β†—

Difficulty

11.765196

Transactions

1

Size

201 B

Version

2

Bits

0bc3e3e5

Nonce

1,937,765,168

Timestamp

5/4/2018, 10:31:37 PM

Confirmations

4,192,961

Merkle Root

43d93baf0f1f3bbeab7936faf4472e6fc04cafd4d6c317d7fad14802a28b5b59
Transactions (1)
Coinbase43d93baf0f1f3b…d14802a28b5b59
1 in β†’ 1 out7.2100 XPM110 B
AaQfMqW6…My5Y919X
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.

2.660 Γ— 10⁹⁢(97-digit number)
26601281016546911197…56695817163306278400
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
2.660 Γ— 10⁹⁢(97-digit number)
26601281016546911197…56695817163306278399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.320 Γ— 10⁹⁢(97-digit number)
53202562033093822395…13391634326612556799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.064 Γ— 10⁹⁷(98-digit number)
10640512406618764479…26783268653225113599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.128 Γ— 10⁹⁷(98-digit number)
21281024813237528958…53566537306450227199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.256 Γ— 10⁹⁷(98-digit number)
42562049626475057916…07133074612900454399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.512 Γ— 10⁹⁷(98-digit number)
85124099252950115833…14266149225800908799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.702 Γ— 10⁹⁸(99-digit number)
17024819850590023166…28532298451601817599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.404 Γ— 10⁹⁸(99-digit number)
34049639701180046333…57064596903203635199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.809 Γ— 10⁹⁸(99-digit number)
68099279402360092666…14129193806407270399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.361 Γ— 10⁹⁹(100-digit number)
13619855880472018533…28258387612814540799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.723 Γ— 10⁹⁹(100-digit number)
27239711760944037066…56516775225629081599
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 2649009

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 67c213882f2e9193223686afba9ade8e6308dadbbfc6b976fbe6574de1bbf7aa

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 #2,649,009 on Chainz β†—
Circulating Supply:57,980,143 XPMΒ·at block #6,841,969 Β· updates every 60s
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