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Home/Chain Registry/Block #1,352,582

Block #1,352,582

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/3/2015, 3:50:27 PM Β· Difficulty 10.7957 Β· 5,459,828 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a4b7ee97104578108e8e749ec984c5a871f9123e6686d96aa071a61ed7ad9e4
View on Chainz β†—

Difficulty

10.795713

Transactions

1

Size

199 B

Version

2

Bits

0acbb3e0

Nonce

360,130,900

Timestamp

12/3/2015, 3:50:27 PM

Confirmations

5,459,828

Merkle Root

e5efb41ac1b7b3e2bef310010e351a72a20065ea8a07995f97860f3267ae295d
Transactions (1)
Coinbasee5efb41ac1b7b3…860f3267ae295d
1 in β†’ 1 out8.5700 XPM109 B
AKdgZNGt…YFCEwQHa
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.

3.799 Γ— 10⁹⁴(95-digit number)
37991060072241238647…06909216460731536480
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
3.799 Γ— 10⁹⁴(95-digit number)
37991060072241238647…06909216460731536481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.598 Γ— 10⁹⁴(95-digit number)
75982120144482477294…13818432921463072961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.519 Γ— 10⁹⁡(96-digit number)
15196424028896495458…27636865842926145921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.039 Γ— 10⁹⁡(96-digit number)
30392848057792990917…55273731685852291841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.078 Γ— 10⁹⁡(96-digit number)
60785696115585981835…10547463371704583681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.215 Γ— 10⁹⁢(97-digit number)
12157139223117196367…21094926743409167361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.431 Γ— 10⁹⁢(97-digit number)
24314278446234392734…42189853486818334721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.862 Γ— 10⁹⁢(97-digit number)
48628556892468785468…84379706973636669441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.725 Γ— 10⁹⁢(97-digit number)
97257113784937570936…68759413947273338881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.945 Γ— 10⁹⁷(98-digit number)
19451422756987514187…37518827894546677761
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 1352582

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 5a4b7ee97104578108e8e749ec984c5a871f9123e6686d96aa071a61ed7ad9e4

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 #1,352,582 on Chainz β†—
Circulating Supply:57,743,307 XPMΒ·at block #6,812,409 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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