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Block #246,436

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/6/2013, 3:20:03 AM Β· Difficulty 9.9643 Β· 6,584,720 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d679e899045ae37f13552c214d7c93dfe52b66630dcca978c12de8270d386b68
View on Chainz β†—

Height

#246,436

Difficulty

9.964262

Transactions

1

Size

207 B

Version

2

Bits

09f6d9df

Nonce

714,606

Timestamp

11/6/2013, 3:20:03 AM

Confirmations

6,584,720

Merkle Root

61e89090758971f28c97aa5f70170703628a763f1172d9e775501f5076732015
Transactions (1)
Coinbase61e89090758971…501f5076732015
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.615 Γ— 10⁹⁸(99-digit number)
16156410758147515764…53549974858324864000
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
1.615 Γ— 10⁹⁸(99-digit number)
16156410758147515764…53549974858324864001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.231 Γ— 10⁹⁸(99-digit number)
32312821516295031529…07099949716649728001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.462 Γ— 10⁹⁸(99-digit number)
64625643032590063059…14199899433299456001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.292 Γ— 10⁹⁹(100-digit number)
12925128606518012611…28399798866598912001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.585 Γ— 10⁹⁹(100-digit number)
25850257213036025223…56799597733197824001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.170 Γ— 10⁹⁹(100-digit number)
51700514426072050447…13599195466395648001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.034 Γ— 10¹⁰⁰(101-digit number)
10340102885214410089…27198390932791296001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.068 Γ— 10¹⁰⁰(101-digit number)
20680205770428820179…54396781865582592001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.136 Γ— 10¹⁰⁰(101-digit number)
41360411540857640358…08793563731165184001
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 246436

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 d679e899045ae37f13552c214d7c93dfe52b66630dcca978c12de8270d386b68

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 #246,436 on Chainz β†—
Circulating Supply:57,893,387 XPMΒ·at block #6,831,155 Β· updates every 60s
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