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Home/Chain Registry/Block #2,862,928

Block #2,862,928

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/1/2018, 5:23:24 PM Β· Difficulty 11.6738 Β· 3,980,915 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9728986a869f3d4078def7bb4968bd1010fd80e445c31bda2d0619a2b37919cb
View on Chainz β†—

Difficulty

11.673781

Transactions

1

Size

200 B

Version

2

Bits

0bac7ce8

Nonce

421,174,371

Timestamp

10/1/2018, 5:23:24 PM

Confirmations

3,980,915

Merkle Root

19afce9b441007d7cf8e2892368d3ec7d2979d3c1d553fad1531b768fbd96671
Transactions (1)
Coinbase19afce9b441007…31b768fbd96671
1 in β†’ 1 out7.3300 XPM110 B
ASDhmmFp…BqFUafZ1
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.

8.813 Γ— 10⁹⁴(95-digit number)
88137670659952398469…66249688626571580800
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
8.813 Γ— 10⁹⁴(95-digit number)
88137670659952398469…66249688626571580799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.762 Γ— 10⁹⁡(96-digit number)
17627534131990479693…32499377253143161599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.525 Γ— 10⁹⁡(96-digit number)
35255068263980959387…64998754506286323199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.051 Γ— 10⁹⁡(96-digit number)
70510136527961918775…29997509012572646399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.410 Γ— 10⁹⁢(97-digit number)
14102027305592383755…59995018025145292799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.820 Γ— 10⁹⁢(97-digit number)
28204054611184767510…19990036050290585599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.640 Γ— 10⁹⁢(97-digit number)
56408109222369535020…39980072100581171199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.128 Γ— 10⁹⁷(98-digit number)
11281621844473907004…79960144201162342399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.256 Γ— 10⁹⁷(98-digit number)
22563243688947814008…59920288402324684799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.512 Γ— 10⁹⁷(98-digit number)
45126487377895628016…19840576804649369599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.025 Γ— 10⁹⁷(98-digit number)
90252974755791256032…39681153609298739199
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 2862928

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 9728986a869f3d4078def7bb4968bd1010fd80e445c31bda2d0619a2b37919cb

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 #2,862,928 on Chainz β†—
Circulating Supply:57,995,110 XPMΒ·at block #6,843,842 Β· updates every 60s
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