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Home/Chain Registry/Block #2,770,684

Block #2,770,684

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/29/2018, 6:40:53 PM Β· Difficulty 11.6596 Β· 4,074,267 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb05be2189b08922666b2c713eb4e6ffb4108be7df0d01a0f3211d5ba8059e83
View on Chainz β†—

Difficulty

11.659608

Transactions

1

Size

201 B

Version

2

Bits

0ba8dc11

Nonce

24,638,621

Timestamp

7/29/2018, 6:40:53 PM

Confirmations

4,074,267

Merkle Root

c23e208513a0725e7daf56f1dbfeb1facb7efd493f234a68ec294ed75d2e9ff2
Transactions (1)
Coinbasec23e208513a072…294ed75d2e9ff2
1 in β†’ 1 out7.3400 XPM110 B
Af68GS9b…wpgA8ovR
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.

1.021 Γ— 10⁹⁢(97-digit number)
10212949451879755575…92762034415017949440
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
1.021 Γ— 10⁹⁢(97-digit number)
10212949451879755575…92762034415017949441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.042 Γ— 10⁹⁢(97-digit number)
20425898903759511150…85524068830035898881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.085 Γ— 10⁹⁢(97-digit number)
40851797807519022300…71048137660071797761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.170 Γ— 10⁹⁢(97-digit number)
81703595615038044600…42096275320143595521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.634 Γ— 10⁹⁷(98-digit number)
16340719123007608920…84192550640287191041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.268 Γ— 10⁹⁷(98-digit number)
32681438246015217840…68385101280574382081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.536 Γ— 10⁹⁷(98-digit number)
65362876492030435680…36770202561148764161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.307 Γ— 10⁹⁸(99-digit number)
13072575298406087136…73540405122297528321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.614 Γ— 10⁹⁸(99-digit number)
26145150596812174272…47080810244595056641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.229 Γ— 10⁹⁸(99-digit number)
52290301193624348544…94161620489190113281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.045 Γ— 10⁹⁹(100-digit number)
10458060238724869708…88323240978380226561
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 2770684

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 cb05be2189b08922666b2c713eb4e6ffb4108be7df0d01a0f3211d5ba8059e83

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 #2,770,684 on Chainz β†—
Circulating Supply:58,004,025 XPMΒ·at block #6,844,950 Β· updates every 60s
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