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Block #2,648,878

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/4/2018, 8:11:41 PM Β· Difficulty 11.7656 Β· 4,190,062 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c3f7e04cfab6d00982c0431359e85be761cc7e77fc43770ed62830c0aa9b3f3
View on Chainz β†—

Difficulty

11.765630

Transactions

1

Size

200 B

Version

2

Bits

0bc4004d

Nonce

585,935,188

Timestamp

5/4/2018, 8:11:41 PM

Confirmations

4,190,062

Merkle Root

33435984173695eb2eeb557097e205584f5ce3068123fede4df2e8cc34f23484
Transactions (1)
Coinbase33435984173695…f2e8cc34f23484
1 in β†’ 1 out7.2100 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.204 Γ— 10⁹⁴(95-digit number)
12049826702944422544…31003830514226444080
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
1.204 Γ— 10⁹⁴(95-digit number)
12049826702944422544…31003830514226444081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.409 Γ— 10⁹⁴(95-digit number)
24099653405888845089…62007661028452888161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.819 Γ— 10⁹⁴(95-digit number)
48199306811777690179…24015322056905776321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.639 Γ— 10⁹⁴(95-digit number)
96398613623555380359…48030644113811552641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.927 Γ— 10⁹⁡(96-digit number)
19279722724711076071…96061288227623105281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.855 Γ— 10⁹⁡(96-digit number)
38559445449422152143…92122576455246210561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.711 Γ— 10⁹⁡(96-digit number)
77118890898844304287…84245152910492421121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.542 Γ— 10⁹⁢(97-digit number)
15423778179768860857…68490305820984842241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.084 Γ— 10⁹⁢(97-digit number)
30847556359537721715…36980611641969684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.169 Γ— 10⁹⁢(97-digit number)
61695112719075443430…73961223283939368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.233 Γ— 10⁹⁷(98-digit number)
12339022543815088686…47922446567878737921
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 2648878

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 7c3f7e04cfab6d00982c0431359e85be761cc7e77fc43770ed62830c0aa9b3f3

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 #2,648,878 on Chainz β†—
Circulating Supply:57,955,785 XPMΒ·at block #6,838,939 Β· updates every 60s
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