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Block #201,806

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/9/2013, 8:32:51 PM Β· Difficulty 9.8932 Β· 6,603,216 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dc8cae500fdbf7c42358f957ff3ee5921a4ba3bfbdcfb14f31cb5328bb4dea4e
View on Chainz β†—

Height

#201,806

Difficulty

9.893173

Transactions

1

Size

200 B

Version

2

Bits

09e4a6f8

Nonce

11,064

Timestamp

10/9/2013, 8:32:51 PM

Confirmations

6,603,216

Merkle Root

0bfc8eebfec341dd734d118997b0f74179651f8e6b80afb64f760dfb2581d712
Transactions (1)
Coinbase0bfc8eebfec341…760dfb2581d712
1 in β†’ 1 out10.2000 XPM110 B
AFvfCa1W…3pZgbFWa
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.

1.253 Γ— 10⁹⁴(95-digit number)
12539305550171718770…83199534182425586480
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
1.253 Γ— 10⁹⁴(95-digit number)
12539305550171718770…83199534182425586481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.507 Γ— 10⁹⁴(95-digit number)
25078611100343437540…66399068364851172961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.015 Γ— 10⁹⁴(95-digit number)
50157222200686875080…32798136729702345921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.003 Γ— 10⁹⁡(96-digit number)
10031444440137375016…65596273459404691841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.006 Γ— 10⁹⁡(96-digit number)
20062888880274750032…31192546918809383681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.012 Γ— 10⁹⁡(96-digit number)
40125777760549500064…62385093837618767361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.025 Γ— 10⁹⁡(96-digit number)
80251555521099000128…24770187675237534721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.605 Γ— 10⁹⁢(97-digit number)
16050311104219800025…49540375350475069441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.210 Γ— 10⁹⁢(97-digit number)
32100622208439600051…99080750700950138881
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 201806

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 dc8cae500fdbf7c42358f957ff3ee5921a4ba3bfbdcfb14f31cb5328bb4dea4e

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 #201,806 on Chainz β†—
Circulating Supply:57,684,240 XPMΒ·at block #6,805,021 Β· updates every 60s
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