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Home/Chain Registry/Block #1,534,636

Block #1,534,636

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 9:19:36 AM Β· Difficulty 10.6170 Β· 5,283,219 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dbf9320c8d35193a8c7e1ab311ca6b3d18beb87e172eaccf522070b671ec04ce
View on Chainz β†—

Difficulty

10.616972

Transactions

1

Size

200 B

Version

2

Bits

0a9df1e5

Nonce

287,733,869

Timestamp

4/10/2016, 9:19:36 AM

Confirmations

5,283,219

Merkle Root

9e770144522e410df38fbfa37d0d1941d873d963adaa321b396341d6e367ee08
Transactions (1)
Coinbase9e770144522e41…6341d6e367ee08
1 in β†’ 1 out8.8600 XPM109 B
AHqXrS92…5MCP6g5T
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.

9.522 Γ— 10⁹⁡(96-digit number)
95223819146665125672…01361378860087833600
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
9.522 Γ— 10⁹⁡(96-digit number)
95223819146665125672…01361378860087833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.904 Γ— 10⁹⁢(97-digit number)
19044763829333025134…02722757720175667201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.808 Γ— 10⁹⁢(97-digit number)
38089527658666050268…05445515440351334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.617 Γ— 10⁹⁢(97-digit number)
76179055317332100537…10891030880702668801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.523 Γ— 10⁹⁷(98-digit number)
15235811063466420107…21782061761405337601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.047 Γ— 10⁹⁷(98-digit number)
30471622126932840215…43564123522810675201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.094 Γ— 10⁹⁷(98-digit number)
60943244253865680430…87128247045621350401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.218 Γ— 10⁹⁸(99-digit number)
12188648850773136086…74256494091242700801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.437 Γ— 10⁹⁸(99-digit number)
24377297701546272172…48512988182485401601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.875 Γ— 10⁹⁸(99-digit number)
48754595403092544344…97025976364970803201
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 1534636

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 dbf9320c8d35193a8c7e1ab311ca6b3d18beb87e172eaccf522070b671ec04ce

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 #1,534,636 on Chainz β†—
Circulating Supply:57,786,906 XPMΒ·at block #6,817,854 Β· updates every 60s
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