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Home/Chain Registry/Block #1,145,815

Block #1,145,815

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/9/2015, 1:10:53 AM Β· Difficulty 10.9318 Β· 5,668,241 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a71c7adf694ff20d51fc827526eda996d4520ad2ebc0bd307baf213d276a4b8d
View on Chainz β†—

Difficulty

10.931835

Transactions

1

Size

201 B

Version

2

Bits

0aee8cbd

Nonce

346,747,156

Timestamp

7/9/2015, 1:10:53 AM

Confirmations

5,668,241

Merkle Root

0732271df6da206c3c8fca9abfaec6aa875feab043e7247f23f8eca7a2b555ca
Transactions (1)
Coinbase0732271df6da20…f8eca7a2b555ca
1 in β†’ 1 out8.3500 XPM110 B
AQmyv2Xy…epAwZKNB
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.

4.925 Γ— 10⁹⁢(97-digit number)
49259902076874736174…16910026627292200960
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
4.925 Γ— 10⁹⁢(97-digit number)
49259902076874736174…16910026627292200961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.851 Γ— 10⁹⁢(97-digit number)
98519804153749472348…33820053254584401921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.970 Γ— 10⁹⁷(98-digit number)
19703960830749894469…67640106509168803841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.940 Γ— 10⁹⁷(98-digit number)
39407921661499788939…35280213018337607681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.881 Γ— 10⁹⁷(98-digit number)
78815843322999577879…70560426036675215361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.576 Γ— 10⁹⁸(99-digit number)
15763168664599915575…41120852073350430721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.152 Γ— 10⁹⁸(99-digit number)
31526337329199831151…82241704146700861441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.305 Γ— 10⁹⁸(99-digit number)
63052674658399662303…64483408293401722881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.261 Γ— 10⁹⁹(100-digit number)
12610534931679932460…28966816586803445761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.522 Γ— 10⁹⁹(100-digit number)
25221069863359864921…57933633173606891521
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 1145815

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 a71c7adf694ff20d51fc827526eda996d4520ad2ebc0bd307baf213d276a4b8d

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 #1,145,815 on Chainz β†—
Circulating Supply:57,756,524 XPMΒ·at block #6,814,055 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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