XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,639,996

Block #2,639,996

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 8:33:54 PM Β· Difficulty 11.5622 Β· 4,193,471 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4d928bd21adc31b80477922b803f52d69d2d3205f88517294bb93fbf39cdc7a3
View on Chainz β†—

Difficulty

11.562177

Transactions

1

Size

200 B

Version

2

Bits

0b8feadc

Nonce

1,469,880,534

Timestamp

4/30/2018, 8:33:54 PM

Confirmations

4,193,471

Merkle Root

b183636ee5f530efea756eaa1e8b19899928d33d145ce98d176d04012e77f0a0
Transactions (1)
Coinbaseb183636ee5f530…6d04012e77f0a0
1 in β†’ 1 out7.4700 XPM110 B
AM22ADpX…YRj8aztR
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.

1.075 Γ— 10⁹⁴(95-digit number)
10758582554268203572…13729481243549570820
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
1.075 Γ— 10⁹⁴(95-digit number)
10758582554268203572…13729481243549570821
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.151 Γ— 10⁹⁴(95-digit number)
21517165108536407145…27458962487099141641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.303 Γ— 10⁹⁴(95-digit number)
43034330217072814291…54917924974198283281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.606 Γ— 10⁹⁴(95-digit number)
86068660434145628582…09835849948396566561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.721 Γ— 10⁹⁡(96-digit number)
17213732086829125716…19671699896793133121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.442 Γ— 10⁹⁡(96-digit number)
34427464173658251433…39343399793586266241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.885 Γ— 10⁹⁡(96-digit number)
68854928347316502866…78686799587172532481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.377 Γ— 10⁹⁢(97-digit number)
13770985669463300573…57373599174345064961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.754 Γ— 10⁹⁢(97-digit number)
27541971338926601146…14747198348690129921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.508 Γ— 10⁹⁢(97-digit number)
55083942677853202292…29494396697380259841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.101 Γ— 10⁹⁷(98-digit number)
11016788535570640458…58988793394760519681
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 2639996

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 4d928bd21adc31b80477922b803f52d69d2d3205f88517294bb93fbf39cdc7a3

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 #2,639,996 on Chainz β†—
Circulating Supply:57,911,937 XPMΒ·at block #6,833,466 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