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Home/Chain Registry/Block #2,750,449

Block #2,750,449

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2018, 8:47:05 PM Β· Difficulty 11.6450 Β· 4,081,970 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
22b33a642d3b12b43aa825c073b0c06da944b7bb6c5033603548495d197376ea
View on Chainz β†—

Difficulty

11.645010

Transactions

1

Size

201 B

Version

2

Bits

0ba51f59

Nonce

71,661,960

Timestamp

7/15/2018, 8:47:05 PM

Confirmations

4,081,970

Merkle Root

55ea6c54b4f058abb29895983b593be59f95290abf3c632705fbea34b391ff5e
Transactions (1)
Coinbase55ea6c54b4f058…fbea34b391ff5e
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.648 Γ— 10⁹⁢(97-digit number)
16480243103620307105…57202615031809996800
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
1.648 Γ— 10⁹⁢(97-digit number)
16480243103620307105…57202615031809996801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.296 Γ— 10⁹⁢(97-digit number)
32960486207240614210…14405230063619993601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.592 Γ— 10⁹⁢(97-digit number)
65920972414481228421…28810460127239987201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.318 Γ— 10⁹⁷(98-digit number)
13184194482896245684…57620920254479974401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.636 Γ— 10⁹⁷(98-digit number)
26368388965792491368…15241840508959948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.273 Γ— 10⁹⁷(98-digit number)
52736777931584982737…30483681017919897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.054 Γ— 10⁹⁸(99-digit number)
10547355586316996547…60967362035839795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.109 Γ— 10⁹⁸(99-digit number)
21094711172633993094…21934724071679590401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.218 Γ— 10⁹⁸(99-digit number)
42189422345267986189…43869448143359180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.437 Γ— 10⁹⁸(99-digit number)
84378844690535972379…87738896286718361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.687 Γ— 10⁹⁹(100-digit number)
16875768938107194475…75477792573436723201
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 2750449

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 22b33a642d3b12b43aa825c073b0c06da944b7bb6c5033603548495d197376ea

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 #2,750,449 on Chainz β†—
Circulating Supply:57,903,499 XPMΒ·at block #6,832,418 Β· updates every 60s
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