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Home/Chain Registry/Block #3,000,206

Block #3,000,206

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/8/2019, 3:12:44 AM Β· Difficulty 11.2222 Β· 3,843,143 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c0a8f8b384cb63c03334a416f1d87b20b2e3f2c4f7371d2174454c33bb8d2f7f
View on Chainz β†—

Difficulty

11.222230

Transactions

1

Size

199 B

Version

2

Bits

0b38e40d

Nonce

927,794,247

Timestamp

1/8/2019, 3:12:44 AM

Confirmations

3,843,143

Merkle Root

8a7ecb827596f1a38bd2c2e3c784c4c7d0fcab727e3f10bdf0468dd6e41a99c3
Transactions (1)
Coinbase8a7ecb827596f1…468dd6e41a99c3
1 in β†’ 1 out7.9300 XPM109 B
AUhjokok…k5m93PZR
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.

4.971 Γ— 10⁹⁡(96-digit number)
49716125020825843322…32421615366844583680
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
4.971 Γ— 10⁹⁡(96-digit number)
49716125020825843322…32421615366844583681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.943 Γ— 10⁹⁡(96-digit number)
99432250041651686645…64843230733689167361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.988 Γ— 10⁹⁢(97-digit number)
19886450008330337329…29686461467378334721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.977 Γ— 10⁹⁢(97-digit number)
39772900016660674658…59372922934756669441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.954 Γ— 10⁹⁢(97-digit number)
79545800033321349316…18745845869513338881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.590 Γ— 10⁹⁷(98-digit number)
15909160006664269863…37491691739026677761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.181 Γ— 10⁹⁷(98-digit number)
31818320013328539726…74983383478053355521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.363 Γ— 10⁹⁷(98-digit number)
63636640026657079452…49966766956106711041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.272 Γ— 10⁹⁸(99-digit number)
12727328005331415890…99933533912213422081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.545 Γ— 10⁹⁸(99-digit number)
25454656010662831781…99867067824426844161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.090 Γ— 10⁹⁸(99-digit number)
50909312021325663562…99734135648853688321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 3000206

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 c0a8f8b384cb63c03334a416f1d87b20b2e3f2c4f7371d2174454c33bb8d2f7f

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 #3,000,206 on Chainz β†—
Circulating Supply:57,991,153 XPMΒ·at block #6,843,348 Β· updates every 60s
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