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Home/Chain Registry/Block #2,828,547

Block #2,828,547

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/7/2018, 9:38:50 AM Β· Difficulty 11.7117 Β· 4,013,697 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4af877d6697e5dcd5bc24d0df5ede552b8b6df5000615915889106307ab5bfa3
View on Chainz β†—

Difficulty

11.711702

Transactions

1

Size

200 B

Version

2

Bits

0bb63219

Nonce

1,157,018,704

Timestamp

9/7/2018, 9:38:50 AM

Confirmations

4,013,697

Merkle Root

363c507380a72aea6d84f970bdc8915edb516960d39d96feacf2e04707c7408b
Transactions (1)
Coinbase363c507380a72a…f2e04707c7408b
1 in β†’ 1 out7.2800 XPM110 B
AXvNKM6r…ytNSK4Z2
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.

9.583 Γ— 10⁹⁴(95-digit number)
95830844777141169280…41978890723055189800
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
9.583 Γ— 10⁹⁴(95-digit number)
95830844777141169280…41978890723055189799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.916 Γ— 10⁹⁡(96-digit number)
19166168955428233856…83957781446110379599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.833 Γ— 10⁹⁡(96-digit number)
38332337910856467712…67915562892220759199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.666 Γ— 10⁹⁡(96-digit number)
76664675821712935424…35831125784441518399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.533 Γ— 10⁹⁢(97-digit number)
15332935164342587084…71662251568883036799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.066 Γ— 10⁹⁢(97-digit number)
30665870328685174169…43324503137766073599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.133 Γ— 10⁹⁢(97-digit number)
61331740657370348339…86649006275532147199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.226 Γ— 10⁹⁷(98-digit number)
12266348131474069667…73298012551064294399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.453 Γ— 10⁹⁷(98-digit number)
24532696262948139335…46596025102128588799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.906 Γ— 10⁹⁷(98-digit number)
49065392525896278671…93192050204257177599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.813 Γ— 10⁹⁷(98-digit number)
98130785051792557343…86384100408514355199
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 2828547

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 4af877d6697e5dcd5bc24d0df5ede552b8b6df5000615915889106307ab5bfa3

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 #2,828,547 on Chainz β†—
Circulating Supply:57,982,350 XPMΒ·at block #6,842,243 Β· updates every 60s
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