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Block #245,406

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/5/2013, 10:56:40 AM Β· Difficulty 9.9639 Β· 6,590,957 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3b8f007e90fe30f35ee2fd75e909bcc59ef4ae1048c4cc85fedf43c192f86219
View on Chainz β†—

Height

#245,406

Difficulty

9.963878

Transactions

1

Size

232 B

Version

2

Bits

09f6c0b8

Nonce

9,372

Timestamp

11/5/2013, 10:56:40 AM

Confirmations

6,590,957

Merkle Root

284765a090663c3ea8e794ee5ce2d8b8db7f90b44e00c5492b2566b41303ed35
Transactions (1)
Coinbase284765a090663c…2566b41303ed35
1 in β†’ 2 out10.0600 XPM142 B
AKcbk49N…GJbKa7j1ALfEGCwh…VawujfMm
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.

1.754 Γ— 10⁹⁴(95-digit number)
17545552505431612579…72410783910132990550
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
1.754 Γ— 10⁹⁴(95-digit number)
17545552505431612579…72410783910132990551
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.509 Γ— 10⁹⁴(95-digit number)
35091105010863225159…44821567820265981101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.018 Γ— 10⁹⁴(95-digit number)
70182210021726450318…89643135640531962201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.403 Γ— 10⁹⁡(96-digit number)
14036442004345290063…79286271281063924401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.807 Γ— 10⁹⁡(96-digit number)
28072884008690580127…58572542562127848801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.614 Γ— 10⁹⁡(96-digit number)
56145768017381160254…17145085124255697601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.122 Γ— 10⁹⁢(97-digit number)
11229153603476232050…34290170248511395201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.245 Γ— 10⁹⁢(97-digit number)
22458307206952464101…68580340497022790401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.491 Γ— 10⁹⁢(97-digit number)
44916614413904928203…37160680994045580801
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 245406

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 3b8f007e90fe30f35ee2fd75e909bcc59ef4ae1048c4cc85fedf43c192f86219

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 #245,406 on Chainz β†—
Circulating Supply:57,935,163 XPMΒ·at block #6,836,362 Β· updates every 60s
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