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Block #290,611

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/2/2013, 6:52:35 PM Β· Difficulty 9.9893 Β· 6,534,587 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7d23d749178694f74db2f3e025bb9cb4636b52c2de8a403b84e3aabae20293c3
View on Chainz β†—

Height

#290,611

Difficulty

9.989328

Transactions

1

Size

206 B

Version

2

Bits

09fd449b

Nonce

33,805

Timestamp

12/2/2013, 6:52:35 PM

Confirmations

6,534,587

Merkle Root

bb7ee2c489ecb5d5c67ccca706a07c2c1b2ba3edc74844e474663428a4dd68fe
Transactions (1)
Coinbasebb7ee2c489ecb5…663428a4dd68fe
1 in β†’ 1 out10.0100 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.

4.307 Γ— 10⁹⁴(95-digit number)
43076293911344112065…30465211909264184660
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
4.307 Γ— 10⁹⁴(95-digit number)
43076293911344112065…30465211909264184661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.615 Γ— 10⁹⁴(95-digit number)
86152587822688224131…60930423818528369321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.723 Γ— 10⁹⁡(96-digit number)
17230517564537644826…21860847637056738641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.446 Γ— 10⁹⁡(96-digit number)
34461035129075289652…43721695274113477281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.892 Γ— 10⁹⁡(96-digit number)
68922070258150579305…87443390548226954561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.378 Γ— 10⁹⁢(97-digit number)
13784414051630115861…74886781096453909121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.756 Γ— 10⁹⁢(97-digit number)
27568828103260231722…49773562192907818241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.513 Γ— 10⁹⁢(97-digit number)
55137656206520463444…99547124385815636481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.102 Γ— 10⁹⁷(98-digit number)
11027531241304092688…99094248771631272961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.205 Γ— 10⁹⁷(98-digit number)
22055062482608185377…98188497543262545921
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 290611

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 7d23d749178694f74db2f3e025bb9cb4636b52c2de8a403b84e3aabae20293c3

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 #290,611 on Chainz β†—
Circulating Supply:57,845,676 XPMΒ·at block #6,825,197 Β· updates every 60s
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