XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #167,698

Block #167,698

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/16/2013, 7:17:07 PM Β· Difficulty 9.8680 Β· 6,650,048 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6d6d4ca8b219e226a0bf865b5bf286b78215f7467cf5bafea47173266c1e9cea
View on Chainz β†—

Height

#167,698

Difficulty

9.868047

Transactions

1

Size

201 B

Version

2

Bits

09de3855

Nonce

15,146

Timestamp

9/16/2013, 7:17:07 PM

Confirmations

6,650,048

Merkle Root

95b181f0d2cad8b7216d1f057d1beab3cd241eca172736be590a79b021e9ebb3
Transactions (1)
Coinbase95b181f0d2cad8…0a79b021e9ebb3
1 in β†’ 1 out10.2500 XPM109 B
AUbvPSMr…YAZUWhFn
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.

7.798 Γ— 10⁹⁸(99-digit number)
77982185096906201365…69730156995425454080
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
7.798 Γ— 10⁹⁸(99-digit number)
77982185096906201365…69730156995425454081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.559 Γ— 10⁹⁹(100-digit number)
15596437019381240273…39460313990850908161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.119 Γ— 10⁹⁹(100-digit number)
31192874038762480546…78920627981701816321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.238 Γ— 10⁹⁹(100-digit number)
62385748077524961092…57841255963403632641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.247 Γ— 10¹⁰⁰(101-digit number)
12477149615504992218…15682511926807265281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.495 Γ— 10¹⁰⁰(101-digit number)
24954299231009984436…31365023853614530561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.990 Γ— 10¹⁰⁰(101-digit number)
49908598462019968873…62730047707229061121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.981 Γ— 10¹⁰⁰(101-digit number)
99817196924039937747…25460095414458122241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.996 Γ— 10¹⁰¹(102-digit number)
19963439384807987549…50920190828916244481
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 167698

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 6d6d4ca8b219e226a0bf865b5bf286b78215f7467cf5bafea47173266c1e9cea

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 #167,698 on Chainz β†—
Circulating Supply:57,786,021 XPMΒ·at block #6,817,745 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.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy