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Home/Chain Registry/Block #2,752,734

Block #2,752,734

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2018, 9:36:05 AM Β· Difficulty 11.6504 Β· 4,088,353 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d0991a3bea0bedd293afe43b782367569eba8e491e31a72954fe5284106c1e5
View on Chainz β†—

Difficulty

11.650401

Transactions

1

Size

199 B

Version

2

Bits

0ba680b3

Nonce

1,389,932,062

Timestamp

7/17/2018, 9:36:05 AM

Confirmations

4,088,353

Merkle Root

dcb47972b1c0c8b18f026088af566e926373fb32030567e67157cb624c03597c
Transactions (1)
Coinbasedcb47972b1c0c8…57cb624c03597c
1 in β†’ 1 out7.3600 XPM110 B
APCgBGe7…zMzEYcYG
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.

1.619 Γ— 10⁹³(94-digit number)
16196723306546831974…06798322045606307500
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
1.619 Γ— 10⁹³(94-digit number)
16196723306546831974…06798322045606307501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.239 Γ— 10⁹³(94-digit number)
32393446613093663948…13596644091212615001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.478 Γ— 10⁹³(94-digit number)
64786893226187327896…27193288182425230001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.295 Γ— 10⁹⁴(95-digit number)
12957378645237465579…54386576364850460001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.591 Γ— 10⁹⁴(95-digit number)
25914757290474931158…08773152729700920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.182 Γ— 10⁹⁴(95-digit number)
51829514580949862317…17546305459401840001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.036 Γ— 10⁹⁡(96-digit number)
10365902916189972463…35092610918803680001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.073 Γ— 10⁹⁡(96-digit number)
20731805832379944926…70185221837607360001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.146 Γ— 10⁹⁡(96-digit number)
41463611664759889853…40370443675214720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.292 Γ— 10⁹⁡(96-digit number)
82927223329519779707…80740887350429440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.658 Γ— 10⁹⁢(97-digit number)
16585444665903955941…61481774700858880001
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 2752734

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 0d0991a3bea0bedd293afe43b782367569eba8e491e31a72954fe5284106c1e5

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 #2,752,734 on Chainz β†—
Circulating Supply:57,973,059 XPMΒ·at block #6,841,086 Β· updates every 60s
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