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Home/Chain Registry/Block #15,936

Block #15,936

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/11/2013, 9:00:42 PM Β· Difficulty 7.8635 Β· 6,809,425 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
05f833d29959fc9908945ef45f2f9eb14b972dea162447c1a63a4be8f3d3cfef
View on Chainz β†—

Height

#15,936

Difficulty

7.863498

Transactions

1

Size

196 B

Version

2

Bits

07dd0e2d

Nonce

252

Timestamp

7/11/2013, 9:00:42 PM

Confirmations

6,809,425

Merkle Root

f36dd9749d6181e5f27546ced778cfedad7bbc6f710227ee010ed2e5b269bc4b
Transactions (1)
Coinbasef36dd9749d6181…0ed2e5b269bc4b
1 in β†’ 1 out16.1500 XPM109 B
AT4HwR3M…1v4hFvRB
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.

3.184 Γ— 10⁸⁸(89-digit number)
31842980253812089067…23670008410786923800
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
3.184 Γ— 10⁸⁸(89-digit number)
31842980253812089067…23670008410786923801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.368 Γ— 10⁸⁸(89-digit number)
63685960507624178134…47340016821573847601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.273 Γ— 10⁸⁹(90-digit number)
12737192101524835626…94680033643147695201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.547 Γ— 10⁸⁹(90-digit number)
25474384203049671253…89360067286295390401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.094 Γ— 10⁸⁹(90-digit number)
50948768406099342507…78720134572590780801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.018 Γ— 10⁹⁰(91-digit number)
10189753681219868501…57440269145181561601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.037 Γ— 10⁹⁰(91-digit number)
20379507362439737002…14880538290363123201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.075 Γ— 10⁹⁰(91-digit number)
40759014724879474005…29761076580726246401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 15936

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 05f833d29959fc9908945ef45f2f9eb14b972dea162447c1a63a4be8f3d3cfef

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 #15,936 on Chainz β†—
Circulating Supply:57,846,994 XPMΒ·at block #6,825,360 Β· updates every 60s
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