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Block #75,290

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 3:32:51 PM Β· Difficulty 8.9960 Β· 6,750,130 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0e9d6a2c1af506b14dc605c8bbff90b86e0640ba12001ee16be79377b7acb8df
View on Chainz β†—

Height

#75,290

Difficulty

8.996020

Transactions

1

Size

201 B

Version

2

Bits

08fefb33

Nonce

569

Timestamp

7/21/2013, 3:32:51 PM

Confirmations

6,750,130

Merkle Root

1ea24e90fc86909dbfd934326aadb00e91a1d979e4c25787f3f3818d668cb647
Transactions (1)
Coinbase1ea24e90fc8690…f3818d668cb647
1 in β†’ 1 out12.3400 XPM110 B
ALhja5Er…uFo3XQuV
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.

2.213 Γ— 10⁹⁢(97-digit number)
22137271144164949682…98081424697449416540
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
2.213 Γ— 10⁹⁢(97-digit number)
22137271144164949682…98081424697449416541
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.427 Γ— 10⁹⁢(97-digit number)
44274542288329899365…96162849394898833081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.854 Γ— 10⁹⁢(97-digit number)
88549084576659798731…92325698789797666161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.770 Γ— 10⁹⁷(98-digit number)
17709816915331959746…84651397579595332321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.541 Γ— 10⁹⁷(98-digit number)
35419633830663919492…69302795159190664641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.083 Γ— 10⁹⁷(98-digit number)
70839267661327838985…38605590318381329281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.416 Γ— 10⁹⁸(99-digit number)
14167853532265567797…77211180636762658561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.833 Γ— 10⁹⁸(99-digit number)
28335707064531135594…54422361273525317121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 75290

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 0e9d6a2c1af506b14dc605c8bbff90b86e0640ba12001ee16be79377b7acb8df

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 #75,290 on Chainz β†—
Circulating Supply:57,847,461 XPMΒ·at block #6,825,419 Β· updates every 60s
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