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Home/Chain Registry/Block #2,096,559

Block #2,096,559

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2017, 1:57:10 AM Β· Difficulty 10.8724 Β· 4,740,236 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
28feaa939d62c1ba6bf105ca8a72e8938850264f3c6bdf1562b7d889a0a13058
View on Chainz β†—

Difficulty

10.872357

Transactions

1

Size

200 B

Version

2

Bits

0adf52c8

Nonce

1,102,182,129

Timestamp

5/2/2017, 1:57:10 AM

Confirmations

4,740,236

Merkle Root

25fce5fbd2b64b850363927ad98ac53d370892221a36c8f4b39f64ad52ea226a
Transactions (1)
Coinbase25fce5fbd2b64b…9f64ad52ea226a
1 in β†’ 1 out8.4500 XPM109 B
ATPLUqcQ…jQZ2m7b5
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.

2.034 Γ— 10⁹⁢(97-digit number)
20348723187642831055…28460850037312509440
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
2.034 Γ— 10⁹⁢(97-digit number)
20348723187642831055…28460850037312509439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.069 Γ— 10⁹⁢(97-digit number)
40697446375285662111…56921700074625018879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.139 Γ— 10⁹⁢(97-digit number)
81394892750571324222…13843400149250037759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.627 Γ— 10⁹⁷(98-digit number)
16278978550114264844…27686800298500075519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.255 Γ— 10⁹⁷(98-digit number)
32557957100228529688…55373600597000151039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.511 Γ— 10⁹⁷(98-digit number)
65115914200457059377…10747201194000302079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.302 Γ— 10⁹⁸(99-digit number)
13023182840091411875…21494402388000604159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.604 Γ— 10⁹⁸(99-digit number)
26046365680182823751…42988804776001208319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.209 Γ— 10⁹⁸(99-digit number)
52092731360365647502…85977609552002416639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.041 Γ— 10⁹⁹(100-digit number)
10418546272073129500…71955219104004833279
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 2096559

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 28feaa939d62c1ba6bf105ca8a72e8938850264f3c6bdf1562b7d889a0a13058

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 #2,096,559 on Chainz β†—
Circulating Supply:57,938,641 XPMΒ·at block #6,836,794 Β· updates every 60s
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