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Home/Chain Registry/Block #2,096,556

Block #2,096,556

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2017, 1:52:38 AM Β· Difficulty 10.8724 Β· 4,740,185 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0f61a709ee854ff1baa6dedc71220c041c249c52ee1d3027d0ca523e78568822
View on Chainz β†—

Difficulty

10.872384

Transactions

1

Size

201 B

Version

2

Bits

0adf5493

Nonce

1,537,318,409

Timestamp

5/2/2017, 1:52:38 AM

Confirmations

4,740,185

Merkle Root

f1ec096189dc880f167ae4002eb78fa7c99b13c0a1020ae512abec3ec47731b5
Transactions (1)
Coinbasef1ec096189dc88…abec3ec47731b5
1 in β†’ 1 out8.4500 XPM110 B
AejvSDQ1…9VSLsv7B
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.

1.674 Γ— 10⁹⁷(98-digit number)
16742802097926218144…35923700605705205760
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
1.674 Γ— 10⁹⁷(98-digit number)
16742802097926218144…35923700605705205759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.348 Γ— 10⁹⁷(98-digit number)
33485604195852436289…71847401211410411519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.697 Γ— 10⁹⁷(98-digit number)
66971208391704872579…43694802422820823039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁸(99-digit number)
13394241678340974515…87389604845641646079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.678 Γ— 10⁹⁸(99-digit number)
26788483356681949031…74779209691283292159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.357 Γ— 10⁹⁸(99-digit number)
53576966713363898063…49558419382566584319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.071 Γ— 10⁹⁹(100-digit number)
10715393342672779612…99116838765133168639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.143 Γ— 10⁹⁹(100-digit number)
21430786685345559225…98233677530266337279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.286 Γ— 10⁹⁹(100-digit number)
42861573370691118450…96467355060532674559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.572 Γ— 10⁹⁹(100-digit number)
85723146741382236901…92934710121065349119
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 2096556

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 0f61a709ee854ff1baa6dedc71220c041c249c52ee1d3027d0ca523e78568822

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 #2,096,556 on Chainz β†—
Circulating Supply:57,938,212 XPMΒ·at block #6,836,740 Β· updates every 60s
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