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Block #305,680

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/11/2013, 3:27:59 PM Β· Difficulty 9.9936 Β· 6,508,545 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ccdb0bb5f77805d0aec8342fdb816b868048e82d54a332b0e9b4a29c44b3b77
View on Chainz β†—

Height

#305,680

Difficulty

9.993650

Transactions

1

Size

209 B

Version

2

Bits

09fe5fd4

Nonce

150,155

Timestamp

12/11/2013, 3:27:59 PM

Confirmations

6,508,545

Merkle Root

1b1861509b6e5c667c7f05489ea71ce50c2247aab559da91f2316f90762e1216
Transactions (1)
Coinbase1b1861509b6e5c…316f90762e1216
1 in β†’ 1 out10.0000 XPM118 B
AWT6gSnv…uagh3hv2
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.

2.651 Γ— 10⁹⁷(98-digit number)
26510064100809173836…73309920496361553660
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
2.651 Γ— 10⁹⁷(98-digit number)
26510064100809173836…73309920496361553661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.302 Γ— 10⁹⁷(98-digit number)
53020128201618347673…46619840992723107321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.060 Γ— 10⁹⁸(99-digit number)
10604025640323669534…93239681985446214641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.120 Γ— 10⁹⁸(99-digit number)
21208051280647339069…86479363970892429281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.241 Γ— 10⁹⁸(99-digit number)
42416102561294678138…72958727941784858561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.483 Γ— 10⁹⁸(99-digit number)
84832205122589356276…45917455883569717121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.696 Γ— 10⁹⁹(100-digit number)
16966441024517871255…91834911767139434241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.393 Γ— 10⁹⁹(100-digit number)
33932882049035742510…83669823534278868481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.786 Γ— 10⁹⁹(100-digit number)
67865764098071485021…67339647068557736961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9
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 305680

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 6ccdb0bb5f77805d0aec8342fdb816b868048e82d54a332b0e9b4a29c44b3b77

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 #305,680 on Chainz β†—
Circulating Supply:57,757,870 XPMΒ·at block #6,814,224 Β· updates every 60s
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