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Home/Chain Registry/Block #1,331,810

Block #1,331,810

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/18/2015, 8:25:59 AM Β· Difficulty 10.8405 Β· 5,463,840 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c7c3f3134acb3ca33065a0a1ca8211c5e54c00d626b57dbd17cacaa181fc1f3d
View on Chainz β†—

Difficulty

10.840541

Transactions

1

Size

243 B

Version

2

Bits

0ad72db5

Nonce

298,763,893

Timestamp

11/18/2015, 8:25:59 AM

Confirmations

5,463,840

Merkle Root

17820e8e2ef6a5eeb276b6a8721f747eff0bd2fce9c03db46fc54cf7a6349740
Transactions (1)
Coinbase17820e8e2ef6a5…c54cf7a6349740
1 in β†’ 2 out8.5000 XPM152 B
AbNVgXWJ…g3uNfMnjALPu3s2c…EJXLjVFh
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.

3.549 Γ— 10⁹⁷(98-digit number)
35499547484722287463…17068402901065369600
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
3.549 Γ— 10⁹⁷(98-digit number)
35499547484722287463…17068402901065369601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.099 Γ— 10⁹⁷(98-digit number)
70999094969444574926…34136805802130739201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.419 Γ— 10⁹⁸(99-digit number)
14199818993888914985…68273611604261478401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.839 Γ— 10⁹⁸(99-digit number)
28399637987777829970…36547223208522956801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.679 Γ— 10⁹⁸(99-digit number)
56799275975555659941…73094446417045913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.135 Γ— 10⁹⁹(100-digit number)
11359855195111131988…46188892834091827201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.271 Γ— 10⁹⁹(100-digit number)
22719710390222263976…92377785668183654401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.543 Γ— 10⁹⁹(100-digit number)
45439420780444527953…84755571336367308801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.087 Γ— 10⁹⁹(100-digit number)
90878841560889055906…69511142672734617601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.817 Γ— 10¹⁰⁰(101-digit number)
18175768312177811181…39022285345469235201
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 1331810

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 c7c3f3134acb3ca33065a0a1ca8211c5e54c00d626b57dbd17cacaa181fc1f3d

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 #1,331,810 on Chainz β†—
Circulating Supply:57,609,271 XPMΒ·at block #6,795,649 Β· updates every 60s
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