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Home/Chain Registry/Block #2,582,780

Block #2,582,780

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/24/2018, 11:07:44 AM Β· Difficulty 11.1429 Β· 4,259,053 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
070e6f1bd5e8fa89b1759cd432b07ddd17d04fc220a8a26886da9445ffc35854
View on Chainz β†—

Difficulty

11.142931

Transactions

1

Size

201 B

Version

2

Bits

0b24971a

Nonce

46,893,829

Timestamp

3/24/2018, 11:07:44 AM

Confirmations

4,259,053

Merkle Root

ec64fa8d4830d4c9f7bf074c458f04d7d1625bfa1703d96bad2e5f88477b53ba
Transactions (1)
Coinbaseec64fa8d4830d4…2e5f88477b53ba
1 in β†’ 1 out8.0400 XPM110 B
Ad95PUGU…rTdpqNoq
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.

7.579 Γ— 10⁹⁷(98-digit number)
75796470750573327054…00129938336323128320
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
7.579 Γ— 10⁹⁷(98-digit number)
75796470750573327054…00129938336323128319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.515 Γ— 10⁹⁸(99-digit number)
15159294150114665410…00259876672646256639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.031 Γ— 10⁹⁸(99-digit number)
30318588300229330821…00519753345292513279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.063 Γ— 10⁹⁸(99-digit number)
60637176600458661643…01039506690585026559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.212 Γ— 10⁹⁹(100-digit number)
12127435320091732328…02079013381170053119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.425 Γ— 10⁹⁹(100-digit number)
24254870640183464657…04158026762340106239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.850 Γ— 10⁹⁹(100-digit number)
48509741280366929314…08316053524680212479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.701 Γ— 10⁹⁹(100-digit number)
97019482560733858629…16632107049360424959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.940 Γ— 10¹⁰⁰(101-digit number)
19403896512146771725…33264214098720849919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.880 Γ— 10¹⁰⁰(101-digit number)
38807793024293543451…66528428197441699839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.761 Γ— 10¹⁰⁰(101-digit number)
77615586048587086903…33056856394883399679
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 2582780

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 070e6f1bd5e8fa89b1759cd432b07ddd17d04fc220a8a26886da9445ffc35854

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 #2,582,780 on Chainz β†—
Circulating Supply:57,979,037 XPMΒ·at block #6,841,832 Β· updates every 60s
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