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Home/Chain Registry/Block #2,106,578

Block #2,106,578

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/8/2017, 12:23:50 PM Β· Difficulty 10.8903 Β· 4,732,823 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ce4ffad7c7eef4b3f7b5f382adec867c1ccf617e74d8ba78a20fb435b458d322
View on Chainz β†—

Difficulty

10.890315

Transactions

1

Size

199 B

Version

2

Bits

0ae3ebac

Nonce

536,507,058

Timestamp

5/8/2017, 12:23:50 PM

Confirmations

4,732,823

Merkle Root

b00192eb50c88895de416557949dce0536b4809a0df943ba029c50e46c55b9f0
Transactions (1)
Coinbaseb00192eb50c888…9c50e46c55b9f0
1 in β†’ 1 out8.4200 XPM109 B
AUH57Swe…jUxGvQM3
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.

5.473 Γ— 10⁹⁴(95-digit number)
54739471654923995770…41692053538706781690
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
5.473 Γ— 10⁹⁴(95-digit number)
54739471654923995770…41692053538706781691
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.094 Γ— 10⁹⁡(96-digit number)
10947894330984799154…83384107077413563381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.189 Γ— 10⁹⁡(96-digit number)
21895788661969598308…66768214154827126761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.379 Γ— 10⁹⁡(96-digit number)
43791577323939196616…33536428309654253521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.758 Γ— 10⁹⁡(96-digit number)
87583154647878393233…67072856619308507041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.751 Γ— 10⁹⁢(97-digit number)
17516630929575678646…34145713238617014081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.503 Γ— 10⁹⁢(97-digit number)
35033261859151357293…68291426477234028161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.006 Γ— 10⁹⁢(97-digit number)
70066523718302714586…36582852954468056321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.401 Γ— 10⁹⁷(98-digit number)
14013304743660542917…73165705908936112641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.802 Γ— 10⁹⁷(98-digit number)
28026609487321085834…46331411817872225281
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2106578

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 ce4ffad7c7eef4b3f7b5f382adec867c1ccf617e74d8ba78a20fb435b458d322

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 #2,106,578 on Chainz β†—
Circulating Supply:57,959,494 XPMΒ·at block #6,839,400 Β· updates every 60s
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