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Home/Chain Registry/Block #2,558,265

Block #2,558,265

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/10/2018, 6:15:49 AM Β· Difficulty 10.9916 Β· 4,282,950 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a7a4af57f6ddde38824253be407381692a3352fbed780d1ff32f39f5eada10cf
View on Chainz β†—

Difficulty

10.991631

Transactions

1

Size

201 B

Version

2

Bits

0afddb86

Nonce

530,726,980

Timestamp

3/10/2018, 6:15:49 AM

Confirmations

4,282,950

Merkle Root

5e93c253f99e7dabde178c9f160551da26573306c6d44be18e9e6f80d9f463bb
Transactions (1)
Coinbase5e93c253f99e7d…9e6f80d9f463bb
1 in β†’ 1 out8.2600 XPM110 B
AN5j4s5s…XU79JMYr
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.

1.540 Γ— 10⁹⁢(97-digit number)
15404793845938440363…38281301813691033600
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
1.540 Γ— 10⁹⁢(97-digit number)
15404793845938440363…38281301813691033599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.080 Γ— 10⁹⁢(97-digit number)
30809587691876880727…76562603627382067199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.161 Γ— 10⁹⁢(97-digit number)
61619175383753761455…53125207254764134399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.232 Γ— 10⁹⁷(98-digit number)
12323835076750752291…06250414509528268799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.464 Γ— 10⁹⁷(98-digit number)
24647670153501504582…12500829019056537599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.929 Γ— 10⁹⁷(98-digit number)
49295340307003009164…25001658038113075199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.859 Γ— 10⁹⁷(98-digit number)
98590680614006018329…50003316076226150399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.971 Γ— 10⁹⁸(99-digit number)
19718136122801203665…00006632152452300799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.943 Γ— 10⁹⁸(99-digit number)
39436272245602407331…00013264304904601599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.887 Γ— 10⁹⁸(99-digit number)
78872544491204814663…00026528609809203199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.577 Γ— 10⁹⁹(100-digit number)
15774508898240962932…00053057219618406399
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 2558265

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 a7a4af57f6ddde38824253be407381692a3352fbed780d1ff32f39f5eada10cf

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 #2,558,265 on Chainz β†—
Circulating Supply:57,974,079 XPMΒ·at block #6,841,214 Β· updates every 60s
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