XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,860,264

Block #2,860,264

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/29/2018, 8:29:02 PM Β· Difficulty 11.6757 Β· 3,984,892 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a0dabfb0a1d186e71de58a177573d88c69a1e2381c93a89a94603835e0440e7a
View on Chainz β†—

Difficulty

11.675669

Transactions

1

Size

200 B

Version

2

Bits

0bacf89f

Nonce

263,921,048

Timestamp

9/29/2018, 8:29:02 PM

Confirmations

3,984,892

Merkle Root

4aca7321c41da071adba37ac46c58ca7331484fbf71c6eba187bf277048a75f8
Transactions (1)
Coinbase4aca7321c41da0…7bf277048a75f8
1 in β†’ 1 out7.3200 XPM110 B
Aavhh1gK…A86zH5cS
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.

9.003 Γ— 10⁹⁡(96-digit number)
90030774402611997396…82140169581287997440
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
9.003 Γ— 10⁹⁡(96-digit number)
90030774402611997396…82140169581287997439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.800 Γ— 10⁹⁢(97-digit number)
18006154880522399479…64280339162575994879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.601 Γ— 10⁹⁢(97-digit number)
36012309761044798958…28560678325151989759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.202 Γ— 10⁹⁢(97-digit number)
72024619522089597917…57121356650303979519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.440 Γ— 10⁹⁷(98-digit number)
14404923904417919583…14242713300607959039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.880 Γ— 10⁹⁷(98-digit number)
28809847808835839166…28485426601215918079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.761 Γ— 10⁹⁷(98-digit number)
57619695617671678333…56970853202431836159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.152 Γ— 10⁹⁸(99-digit number)
11523939123534335666…13941706404863672319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.304 Γ— 10⁹⁸(99-digit number)
23047878247068671333…27883412809727344639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.609 Γ— 10⁹⁸(99-digit number)
46095756494137342667…55766825619454689279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.219 Γ— 10⁹⁸(99-digit number)
92191512988274685334…11533651238909378559
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 2860264

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 a0dabfb0a1d186e71de58a177573d88c69a1e2381c93a89a94603835e0440e7a

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 #2,860,264 on Chainz β†—
Circulating Supply:58,005,676 XPMΒ·at block #6,845,155 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy