XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,887,130

Block #2,887,130

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/19/2018, 1:35:20 AM Β· Difficulty 11.6209 Β· 3,956,681 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3ab08428d58f5e9d2c96f7dcc6ea178e176ac9c7317f01a80ed27bfbcb649a51
View on Chainz β†—

Difficulty

11.620865

Transactions

1

Size

199 B

Version

2

Bits

0b9ef106

Nonce

1,385,778,016

Timestamp

10/19/2018, 1:35:20 AM

Confirmations

3,956,681

Merkle Root

66838ab399aaa379ba5b21535935ca3069ed69eda8d8b42ada3b61b9cb002f8b
Transactions (1)
Coinbase66838ab399aaa3…3b61b9cb002f8b
1 in β†’ 1 out7.3900 XPM110 B
AUMQRepm…tAfKmdW1
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.

2.264 Γ— 10⁹³(94-digit number)
22640602351082924822…75237185333300417760
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
2.264 Γ— 10⁹³(94-digit number)
22640602351082924822…75237185333300417761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.528 Γ— 10⁹³(94-digit number)
45281204702165849645…50474370666600835521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.056 Γ— 10⁹³(94-digit number)
90562409404331699290…00948741333201671041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.811 Γ— 10⁹⁴(95-digit number)
18112481880866339858…01897482666403342081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.622 Γ— 10⁹⁴(95-digit number)
36224963761732679716…03794965332806684161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.244 Γ— 10⁹⁴(95-digit number)
72449927523465359432…07589930665613368321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.448 Γ— 10⁹⁡(96-digit number)
14489985504693071886…15179861331226736641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.897 Γ— 10⁹⁡(96-digit number)
28979971009386143772…30359722662453473281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.795 Γ— 10⁹⁡(96-digit number)
57959942018772287545…60719445324906946561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.159 Γ— 10⁹⁢(97-digit number)
11591988403754457509…21438890649813893121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.318 Γ— 10⁹⁢(97-digit number)
23183976807508915018…42877781299627786241
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2887130

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 3ab08428d58f5e9d2c96f7dcc6ea178e176ac9c7317f01a80ed27bfbcb649a51

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 #2,887,130 on Chainz β†—
Circulating Supply:57,994,863 XPMΒ·at block #6,843,810 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