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Block #13,730

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/11/2013, 2:17:37 PM Β· Difficulty 7.8047 Β· 6,781,797 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3eef7fe6a3eda9716321f59fba2a0fb370b8b3a0932fcd73d5a38fd5ffd9f7a7
View on Chainz β†—

Height

#13,730

Difficulty

7.804697

Transactions

1

Size

194 B

Version

2

Bits

07ce00a0

Nonce

245

Timestamp

7/11/2013, 2:17:37 PM

Confirmations

6,781,797

Merkle Root

70801c731c7c85c0cde68187355c1856f3110311049e77c2d7021480ab23896f
Transactions (1)
Coinbase70801c731c7c85…021480ab23896f
1 in β†’ 1 out16.4000 XPM108 B
AeAHxgid…v9n7DrM8
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.

4.662 Γ— 10⁸⁡(86-digit number)
46627752254771770995…59489934768906251480
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
4.662 Γ— 10⁸⁡(86-digit number)
46627752254771770995…59489934768906251481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.325 Γ— 10⁸⁡(86-digit number)
93255504509543541991…18979869537812502961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.865 Γ— 10⁸⁢(87-digit number)
18651100901908708398…37959739075625005921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.730 Γ— 10⁸⁢(87-digit number)
37302201803817416796…75919478151250011841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.460 Γ— 10⁸⁢(87-digit number)
74604403607634833593…51838956302500023681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.492 Γ— 10⁸⁷(88-digit number)
14920880721526966718…03677912605000047361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.984 Γ— 10⁸⁷(88-digit number)
29841761443053933437…07355825210000094721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.968 Γ— 10⁸⁷(88-digit number)
59683522886107866874…14711650420000189441
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 13730

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 3eef7fe6a3eda9716321f59fba2a0fb370b8b3a0932fcd73d5a38fd5ffd9f7a7

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 #13,730 on Chainz β†—
Circulating Supply:57,608,278 XPMΒ·at block #6,795,526 Β· updates every 60s
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