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Home/Chain Registry/Block #2,056,517

Block #2,056,517

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/5/2017, 9:53:01 AM Β· Difficulty 10.8218 Β· 4,780,256 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
79feb6eb5b862b2ce9b85acdcdc2aa8f588e818996d2c4a77f6ffb4604156fe4
View on Chainz β†—

Difficulty

10.821752

Transactions

1

Size

198 B

Version

2

Bits

0ad25e57

Nonce

1,129,371,283

Timestamp

4/5/2017, 9:53:01 AM

Confirmations

4,780,256

Merkle Root

82de7c3052bdee0afa638addd0d3ad4286852a077ab23bffeff60b7b2d78b307
Transactions (1)
Coinbase82de7c3052bdee…f60b7b2d78b307
1 in β†’ 1 out8.5300 XPM109 B
ALEqc8uA…RotiAbZo
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.

3.610 Γ— 10⁹³(94-digit number)
36107929799089982077…10939877072224225130
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
3.610 Γ— 10⁹³(94-digit number)
36107929799089982077…10939877072224225129
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.221 Γ— 10⁹³(94-digit number)
72215859598179964155…21879754144448450259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.444 Γ— 10⁹⁴(95-digit number)
14443171919635992831…43759508288896900519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.888 Γ— 10⁹⁴(95-digit number)
28886343839271985662…87519016577793801039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.777 Γ— 10⁹⁴(95-digit number)
57772687678543971324…75038033155587602079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.155 Γ— 10⁹⁡(96-digit number)
11554537535708794264…50076066311175204159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.310 Γ— 10⁹⁡(96-digit number)
23109075071417588529…00152132622350408319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.621 Γ— 10⁹⁡(96-digit number)
46218150142835177059…00304265244700816639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.243 Γ— 10⁹⁡(96-digit number)
92436300285670354119…00608530489401633279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.848 Γ— 10⁹⁢(97-digit number)
18487260057134070823…01217060978803266559
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 2056517

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 79feb6eb5b862b2ce9b85acdcdc2aa8f588e818996d2c4a77f6ffb4604156fe4

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 #2,056,517 on Chainz β†—
Circulating Supply:57,938,461 XPMΒ·at block #6,836,772 Β· updates every 60s
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