XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,056,519

Block #2,056,519

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/5/2017, 9:55:18 AM Β· Difficulty 10.8217 Β· 4,780,202 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d83634b97ccc2cb9fddca189aa1363fe16ab380678ff626c34e36a2b1dbc6f73
View on Chainz β†—

Difficulty

10.821721

Transactions

1

Size

199 B

Version

2

Bits

0ad25c4c

Nonce

722,514,400

Timestamp

4/5/2017, 9:55:18 AM

Confirmations

4,780,202

Merkle Root

6382a97ff79c910e39b581775e89ecb70b21b29524bab59c60ace2a41e720c64
Transactions (1)
Coinbase6382a97ff79c91…ace2a41e720c64
1 in β†’ 1 out8.5300 XPM109 B
AVKHgAtS…9fEQrCKU
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.

6.162 Γ— 10⁹⁡(96-digit number)
61624843031828825013…92108101347677204480
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
6.162 Γ— 10⁹⁡(96-digit number)
61624843031828825013…92108101347677204479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.232 Γ— 10⁹⁢(97-digit number)
12324968606365765002…84216202695354408959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.464 Γ— 10⁹⁢(97-digit number)
24649937212731530005…68432405390708817919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.929 Γ— 10⁹⁢(97-digit number)
49299874425463060011…36864810781417635839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.859 Γ— 10⁹⁢(97-digit number)
98599748850926120022…73729621562835271679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.971 Γ— 10⁹⁷(98-digit number)
19719949770185224004…47459243125670543359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.943 Γ— 10⁹⁷(98-digit number)
39439899540370448008…94918486251341086719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.887 Γ— 10⁹⁷(98-digit number)
78879799080740896017…89836972502682173439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.577 Γ— 10⁹⁸(99-digit number)
15775959816148179203…79673945005364346879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.155 Γ— 10⁹⁸(99-digit number)
31551919632296358407…59347890010728693759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2056519

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 d83634b97ccc2cb9fddca189aa1363fe16ab380678ff626c34e36a2b1dbc6f73

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 #2,056,519 on Chainz β†—
Circulating Supply:57,938,050 XPMΒ·at block #6,836,720 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