XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #167,194

Block #167,194

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/16/2013, 10:23:17 AM Β· Difficulty 9.8689 Β· 6,633,051 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2d37a1ef001fefadc346d5f204b67186b4d597916fe42e0ef2b091d2dceefc65
View on Chainz β†—

Height

#167,194

Difficulty

9.868850

Transactions

2

Size

870 B

Version

2

Bits

09de6cf6

Nonce

274,464

Timestamp

9/16/2013, 10:23:17 AM

Confirmations

6,633,051

Merkle Root

d6a43b864d4cae76465eb9187ebb60e363d104c7514dc5699a332168a8566679
Transactions (2)
Coinbasee122c8f15775d3…eacd1eec19ebcd
1 in β†’ 1 out10.2600 XPM109 B
APjeTiVW…u3ADM7uZ
284f2649485221…69b47471757712
4 in β†’ 2 out3.1197 XPM670 B
AWBSLWRK…ncoNmKnJAGnn1YG3…2NddtZvv
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.

1.017 Γ— 10⁹⁷(98-digit number)
10177427396757308565…56928830301894828800
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
1.017 Γ— 10⁹⁷(98-digit number)
10177427396757308565…56928830301894828801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.035 Γ— 10⁹⁷(98-digit number)
20354854793514617130…13857660603789657601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.070 Γ— 10⁹⁷(98-digit number)
40709709587029234260…27715321207579315201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.141 Γ— 10⁹⁷(98-digit number)
81419419174058468521…55430642415158630401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.628 Γ— 10⁹⁸(99-digit number)
16283883834811693704…10861284830317260801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.256 Γ— 10⁹⁸(99-digit number)
32567767669623387408…21722569660634521601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.513 Γ— 10⁹⁸(99-digit number)
65135535339246774817…43445139321269043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.302 Γ— 10⁹⁹(100-digit number)
13027107067849354963…86890278642538086401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.605 Γ— 10⁹⁹(100-digit number)
26054214135698709926…73780557285076172801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.210 Γ— 10⁹⁹(100-digit number)
52108428271397419853…47561114570152345601
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 167194

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 2d37a1ef001fefadc346d5f204b67186b4d597916fe42e0ef2b091d2dceefc65

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 #167,194 on Chainz β†—
Circulating Supply:57,646,014 XPMΒ·at block #6,800,244 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK