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Home/Chain Registry/Block #294,921

Block #294,921

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/5/2013, 3:59:46 AM Β· Difficulty 9.9912 Β· 6,519,155 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0399c54f17190a5bf9cecd65af66e76f18277d88894da32ab63316db33cc9bab
View on Chainz β†—

Height

#294,921

Difficulty

9.991171

Transactions

1

Size

207 B

Version

2

Bits

09fdbd69

Nonce

270,816

Timestamp

12/5/2013, 3:59:46 AM

Confirmations

6,519,155

Merkle Root

cf32ac0294552f909b1c660583e6a3767a95ec715c9a8fd6788d45220c220f50
Transactions (1)
Coinbasecf32ac0294552f…8d45220c220f50
1 in β†’ 1 out10.0000 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.

2.422 Γ— 10⁹⁷(98-digit number)
24224283996180524841…52299832753999012690
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
2.422 Γ— 10⁹⁷(98-digit number)
24224283996180524841…52299832753999012691
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.844 Γ— 10⁹⁷(98-digit number)
48448567992361049683…04599665507998025381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.689 Γ— 10⁹⁷(98-digit number)
96897135984722099366…09199331015996050761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.937 Γ— 10⁹⁸(99-digit number)
19379427196944419873…18398662031992101521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.875 Γ— 10⁹⁸(99-digit number)
38758854393888839746…36797324063984203041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.751 Γ— 10⁹⁸(99-digit number)
77517708787777679493…73594648127968406081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.550 Γ— 10⁹⁹(100-digit number)
15503541757555535898…47189296255936812161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.100 Γ— 10⁹⁹(100-digit number)
31007083515111071797…94378592511873624321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.201 Γ— 10⁹⁹(100-digit number)
62014167030222143594…88757185023747248641
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 294921

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 0399c54f17190a5bf9cecd65af66e76f18277d88894da32ab63316db33cc9bab

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 #294,921 on Chainz β†—
Circulating Supply:57,756,688 XPMΒ·at block #6,814,075 Β· updates every 60s
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