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Block #206,655

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2013, 10:51:53 PM Β· Difficulty 9.9015 Β· 6,588,131 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
88cccc5ecd920204fd5a5a0c5ea04cff2c8acff173ef8bd921e56c151f6c352f
View on Chainz β†—

Height

#206,655

Difficulty

9.901474

Transactions

1

Size

201 B

Version

2

Bits

09e6c708

Nonce

138,611

Timestamp

10/12/2013, 10:51:53 PM

Confirmations

6,588,131

Merkle Root

5ec993211f8181eaf41566d893281a815095855aa18966459040ef6200b1c403
Transactions (1)
Coinbase5ec993211f8181…40ef6200b1c403
1 in β†’ 1 out10.1800 XPM109 B
ATK4r8Gh…Usic4A9N
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.

3.242 Γ— 10⁹⁹(100-digit number)
32429191335234274312…46435145519855656280
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
3.242 Γ— 10⁹⁹(100-digit number)
32429191335234274312…46435145519855656281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.485 Γ— 10⁹⁹(100-digit number)
64858382670468548624…92870291039711312561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.297 Γ— 10¹⁰⁰(101-digit number)
12971676534093709724…85740582079422625121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.594 Γ— 10¹⁰⁰(101-digit number)
25943353068187419449…71481164158845250241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.188 Γ— 10¹⁰⁰(101-digit number)
51886706136374838899…42962328317690500481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.037 Γ— 10¹⁰¹(102-digit number)
10377341227274967779…85924656635381000961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.075 Γ— 10¹⁰¹(102-digit number)
20754682454549935559…71849313270762001921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.150 Γ— 10¹⁰¹(102-digit number)
41509364909099871119…43698626541524003841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.301 Γ— 10¹⁰¹(102-digit number)
83018729818199742239…87397253083048007681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 206655

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 88cccc5ecd920204fd5a5a0c5ea04cff2c8acff173ef8bd921e56c151f6c352f

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 #206,655 on Chainz β†—
Circulating Supply:57,602,341 XPMΒ·at block #6,794,785 Β· updates every 60s
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