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Home/Chain Registry/Block #2,757,735

Block #2,757,735

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2018, 4:52:44 PM Β· Difficulty 11.6671 Β· 4,084,511 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0bd93c1d77845f547e1bd5a83cb151da6b319eaf982b027f81274b7769fa0937
View on Chainz β†—

Difficulty

11.667110

Transactions

1

Size

200 B

Version

2

Bits

0baac7b9

Nonce

805,443,914

Timestamp

7/20/2018, 4:52:44 PM

Confirmations

4,084,511

Merkle Root

25a095270ca8a6cb48e4b501f3a1a54649753f4320208cbc7004ce4aa5814e11
Transactions (1)
Coinbase25a095270ca8a6…04ce4aa5814e11
1 in β†’ 1 out7.3300 XPM110 B
AT8A56Yt…7eDVKRav
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.

5.171 Γ— 10⁹⁡(96-digit number)
51719832982111997327…77329691256150647040
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
5.171 Γ— 10⁹⁡(96-digit number)
51719832982111997327…77329691256150647041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.034 Γ— 10⁹⁢(97-digit number)
10343966596422399465…54659382512301294081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.068 Γ— 10⁹⁢(97-digit number)
20687933192844798930…09318765024602588161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.137 Γ— 10⁹⁢(97-digit number)
41375866385689597861…18637530049205176321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.275 Γ— 10⁹⁢(97-digit number)
82751732771379195723…37275060098410352641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.655 Γ— 10⁹⁷(98-digit number)
16550346554275839144…74550120196820705281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.310 Γ— 10⁹⁷(98-digit number)
33100693108551678289…49100240393641410561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.620 Γ— 10⁹⁷(98-digit number)
66201386217103356578…98200480787282821121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.324 Γ— 10⁹⁸(99-digit number)
13240277243420671315…96400961574565642241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.648 Γ— 10⁹⁸(99-digit number)
26480554486841342631…92801923149131284481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.296 Γ— 10⁹⁸(99-digit number)
52961108973682685263…85603846298262568961
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 2757735

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 0bd93c1d77845f547e1bd5a83cb151da6b319eaf982b027f81274b7769fa0937

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 #2,757,735 on Chainz β†—
Circulating Supply:57,982,366 XPMΒ·at block #6,842,245 Β· updates every 60s
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