XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #170,717

Block #170,717

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/18/2013, 11:40:34 PM Β· Difficulty 9.8650 Β· 6,641,630 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
23ce654dcf1851e8d697a9eafd508f1f9988f970c4ffae4bfda010dacab60be6
View on Chainz β†—

Height

#170,717

Difficulty

9.864973

Transactions

1

Size

200 B

Version

2

Bits

09dd6ed9

Nonce

166,867

Timestamp

9/18/2013, 11:40:34 PM

Confirmations

6,641,630

Merkle Root

82a24d3da569d777bb9f6a2df1d9eb5c6edb3f518208169d64f65d7d6aaf6559
Transactions (1)
Coinbase82a24d3da569d7…f65d7d6aaf6559
1 in β†’ 1 out10.2600 XPM109 B
Ae6PYBDN…jSQhB18y
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.

3.104 Γ— 10⁹⁷(98-digit number)
31048661167955306673…30575642965369584640
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
3.104 Γ— 10⁹⁷(98-digit number)
31048661167955306673…30575642965369584641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.209 Γ— 10⁹⁷(98-digit number)
62097322335910613346…61151285930739169281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.241 Γ— 10⁹⁸(99-digit number)
12419464467182122669…22302571861478338561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.483 Γ— 10⁹⁸(99-digit number)
24838928934364245338…44605143722956677121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.967 Γ— 10⁹⁸(99-digit number)
49677857868728490677…89210287445913354241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.935 Γ— 10⁹⁸(99-digit number)
99355715737456981354…78420574891826708481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.987 Γ— 10⁹⁹(100-digit number)
19871143147491396270…56841149783653416961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.974 Γ— 10⁹⁹(100-digit number)
39742286294982792541…13682299567306833921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.948 Γ— 10⁹⁹(100-digit number)
79484572589965585083…27364599134613667841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.589 Γ— 10¹⁰⁰(101-digit number)
15896914517993117016…54729198269227335681
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 170717

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 23ce654dcf1851e8d697a9eafd508f1f9988f970c4ffae4bfda010dacab60be6

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 #170,717 on Chainz β†—
Circulating Supply:57,742,796 XPMΒ·at block #6,812,346 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

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