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Home/Chain Registry/Block #2,236,739

Block #2,236,739

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/4/2017, 2:27:25 PM Β· Difficulty 10.9463 Β· 4,606,344 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1298af2b6d9798118ea3da5f01959c57896350b506c236f72bbc4d76bf33ac63
View on Chainz β†—

Difficulty

10.946331

Transactions

2

Size

573 B

Version

2

Bits

0af242c4

Nonce

369,864,735

Timestamp

8/4/2017, 2:27:25 PM

Confirmations

4,606,344

Merkle Root

cc9af8220ceb45d1d14c63f362de697ff2d2c74c16376fe7e09d934276365c7b
Transactions (2)
Coinbase9dd057bd9c07a2…439cc51ad6a6d6
1 in β†’ 1 out8.3400 XPM110 B
AKQZXrWQ…3Un3a3pz
7051bf15bb4a5b…2c3a6d45725251
2 in β†’ 2 out409.8800 XPM373 B
AKMZVdTB…kM6MDK6hAesaHg9U…6tjRExna
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.

1.831 Γ— 10⁹⁡(96-digit number)
18310732951315364576…14164532693896534080
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
1.831 Γ— 10⁹⁡(96-digit number)
18310732951315364576…14164532693896534081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.662 Γ— 10⁹⁡(96-digit number)
36621465902630729153…28329065387793068161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.324 Γ— 10⁹⁡(96-digit number)
73242931805261458306…56658130775586136321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.464 Γ— 10⁹⁢(97-digit number)
14648586361052291661…13316261551172272641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.929 Γ— 10⁹⁢(97-digit number)
29297172722104583322…26632523102344545281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.859 Γ— 10⁹⁢(97-digit number)
58594345444209166644…53265046204689090561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.171 Γ— 10⁹⁷(98-digit number)
11718869088841833328…06530092409378181121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.343 Γ— 10⁹⁷(98-digit number)
23437738177683666657…13060184818756362241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.687 Γ— 10⁹⁷(98-digit number)
46875476355367333315…26120369637512724481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.375 Γ— 10⁹⁷(98-digit number)
93750952710734666631…52240739275025448961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2236739

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 1298af2b6d9798118ea3da5f01959c57896350b506c236f72bbc4d76bf33ac63

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 #2,236,739 on Chainz β†—
Circulating Supply:57,989,025 XPMΒ·at block #6,843,082 Β· updates every 60s
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