XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #161,183

Block #161,183

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2013, 12:06:32 PM Β· Difficulty 9.8591 Β· 6,665,846 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d26fbffa1be2fcadcfd2c0489a315a1f0240a4a7d4bfec5c0fc09ca26df8d6e4
View on Chainz β†—

Height

#161,183

Difficulty

9.859077

Transactions

1

Size

199 B

Version

2

Bits

09dbec71

Nonce

321,165

Timestamp

9/12/2013, 12:06:32 PM

Confirmations

6,665,846

Merkle Root

0cef85a3106cc2096dcc6528eb58b1d38cd1a5b95c1ab4147563dcd28f058a74
Transactions (1)
Coinbase0cef85a3106cc2…63dcd28f058a74
1 in β†’ 1 out10.2700 XPM109 B
AHVMSuFn…jNCGMmFs
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.

1.775 Γ— 10⁹⁴(95-digit number)
17758009845787476325…64723737533914599600
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
1.775 Γ— 10⁹⁴(95-digit number)
17758009845787476325…64723737533914599601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.551 Γ— 10⁹⁴(95-digit number)
35516019691574952650…29447475067829199201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.103 Γ— 10⁹⁴(95-digit number)
71032039383149905300…58894950135658398401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.420 Γ— 10⁹⁡(96-digit number)
14206407876629981060…17789900271316796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.841 Γ— 10⁹⁡(96-digit number)
28412815753259962120…35579800542633593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.682 Γ— 10⁹⁡(96-digit number)
56825631506519924240…71159601085267187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.136 Γ— 10⁹⁢(97-digit number)
11365126301303984848…42319202170534374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.273 Γ— 10⁹⁢(97-digit number)
22730252602607969696…84638404341068748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.546 Γ— 10⁹⁢(97-digit number)
45460505205215939392…69276808682137497601
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 161183

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 d26fbffa1be2fcadcfd2c0489a315a1f0240a4a7d4bfec5c0fc09ca26df8d6e4

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 #161,183 on Chainz β†—
Circulating Supply:57,860,412 XPMΒ·at block #6,827,028 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