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Home/Chain Registry/Block #2,557,918

Block #2,557,918

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/10/2018, 1:40:45 AM Β· Difficulty 10.9915 Β· 4,273,557 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6bcef3a499dfa677ccb356491e55f9b0619684e7c82b80ee749d11fa86a00e72
View on Chainz β†—

Difficulty

10.991501

Transactions

2

Size

505 B

Version

2

Bits

0afdd30a

Nonce

804,300,580

Timestamp

3/10/2018, 1:40:45 AM

Confirmations

4,273,557

Merkle Root

84f6f4054d3a2c180e08d9b78050d627142eda1d2576b29af8d0174b2827a20a
Transactions (2)
Coinbasebecc8f2a5621df…77d615a89c3c8d
1 in β†’ 1 out8.2700 XPM109 B
Ac798rYg…sPMZAVWE
6eabfc6f6b2f6e…f1499b98413f7c
2 in β†’ 2 out16.5300 XPM306 B
ATEy9cxL…LgviB6pFAWvLu6Kd…t9saouW4
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.

2.690 Γ— 10⁹⁴(95-digit number)
26906306060519502907…15805383337342958720
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
2.690 Γ— 10⁹⁴(95-digit number)
26906306060519502907…15805383337342958719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.381 Γ— 10⁹⁴(95-digit number)
53812612121039005814…31610766674685917439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.076 Γ— 10⁹⁡(96-digit number)
10762522424207801162…63221533349371834879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.152 Γ— 10⁹⁡(96-digit number)
21525044848415602325…26443066698743669759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.305 Γ— 10⁹⁡(96-digit number)
43050089696831204651…52886133397487339519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.610 Γ— 10⁹⁡(96-digit number)
86100179393662409302…05772266794974679039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.722 Γ— 10⁹⁢(97-digit number)
17220035878732481860…11544533589949358079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.444 Γ— 10⁹⁢(97-digit number)
34440071757464963721…23089067179898716159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.888 Γ— 10⁹⁢(97-digit number)
68880143514929927442…46178134359797432319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.377 Γ— 10⁹⁷(98-digit number)
13776028702985985488…92356268719594864639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.755 Γ— 10⁹⁷(98-digit number)
27552057405971970976…84712537439189729279
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 2557918

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 6bcef3a499dfa677ccb356491e55f9b0619684e7c82b80ee749d11fa86a00e72

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 #2,557,918 on Chainz β†—
Circulating Supply:57,895,891 XPMΒ·at block #6,831,474 Β· updates every 60s
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