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Home/Chain Registry/Block #2,851,521

Block #2,851,521

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/23/2018, 4:30:01 AM Β· Difficulty 11.7260 Β· 3,982,105 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8a78e4d52339d5ca9be4680a21ae49f9e11a3cc496c4b4f6a591da2fabc6b0f3
View on Chainz β†—

Difficulty

11.726040

Transactions

1

Size

200 B

Version

2

Bits

0bb9ddc4

Nonce

1,735,971,186

Timestamp

9/23/2018, 4:30:01 AM

Confirmations

3,982,105

Merkle Root

dc4ff006a2563e54d557ad4d58ab83949fc1f43a32e8bde0f7cff9ef86aecbc8
Transactions (1)
Coinbasedc4ff006a2563e…cff9ef86aecbc8
1 in β†’ 1 out7.2600 XPM110 B
AZxhkKVH…WDWMvjt8
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.

6.887 Γ— 10⁹⁴(95-digit number)
68872307838336949533…48390714333462363520
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
6.887 Γ— 10⁹⁴(95-digit number)
68872307838336949533…48390714333462363521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.377 Γ— 10⁹⁡(96-digit number)
13774461567667389906…96781428666924727041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.754 Γ— 10⁹⁡(96-digit number)
27548923135334779813…93562857333849454081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.509 Γ— 10⁹⁡(96-digit number)
55097846270669559626…87125714667698908161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.101 Γ— 10⁹⁢(97-digit number)
11019569254133911925…74251429335397816321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.203 Γ— 10⁹⁢(97-digit number)
22039138508267823850…48502858670795632641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.407 Γ— 10⁹⁢(97-digit number)
44078277016535647701…97005717341591265281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.815 Γ— 10⁹⁢(97-digit number)
88156554033071295402…94011434683182530561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.763 Γ— 10⁹⁷(98-digit number)
17631310806614259080…88022869366365061121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.526 Γ— 10⁹⁷(98-digit number)
35262621613228518161…76045738732730122241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.052 Γ— 10⁹⁷(98-digit number)
70525243226457036322…52091477465460244481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.410 Γ— 10⁹⁸(99-digit number)
14105048645291407264…04182954930920488961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2851521

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 8a78e4d52339d5ca9be4680a21ae49f9e11a3cc496c4b4f6a591da2fabc6b0f3

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 #2,851,521 on Chainz β†—
Circulating Supply:57,913,218 XPMΒ·at block #6,833,625 Β· updates every 60s
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