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Home/Chain Registry/Block #1,584,350

Block #1,584,350

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/14/2016, 2:47:32 PM Β· Difficulty 10.6503 Β· 5,258,985 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f59d350a89ea37c567ac59c03243cee0cb8362f4e593de500f266ecd2d2955e7
View on Chainz β†—

Difficulty

10.650321

Transactions

1

Size

242 B

Version

2

Bits

0aa67b6b

Nonce

106,477,725

Timestamp

5/14/2016, 2:47:32 PM

Confirmations

5,258,985

Merkle Root

ac06a5952efeb87776473a97708b919bca74f3fb1e6df9a0c55db531ff2d87bd
Transactions (1)
Coinbaseac06a5952efeb8…5db531ff2d87bd
1 in β†’ 2 out8.8000 XPM152 B
AeNeFst2…6pebBnhdALPu3s2c…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.

2.162 Γ— 10⁹⁡(96-digit number)
21626645316959406976…05325489780322701800
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
2.162 Γ— 10⁹⁡(96-digit number)
21626645316959406976…05325489780322701801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.325 Γ— 10⁹⁡(96-digit number)
43253290633918813953…10650979560645403601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.650 Γ— 10⁹⁡(96-digit number)
86506581267837627907…21301959121290807201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.730 Γ— 10⁹⁢(97-digit number)
17301316253567525581…42603918242581614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.460 Γ— 10⁹⁢(97-digit number)
34602632507135051163…85207836485163228801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.920 Γ— 10⁹⁢(97-digit number)
69205265014270102326…70415672970326457601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.384 Γ— 10⁹⁷(98-digit number)
13841053002854020465…40831345940652915201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.768 Γ— 10⁹⁷(98-digit number)
27682106005708040930…81662691881305830401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.536 Γ— 10⁹⁷(98-digit number)
55364212011416081860…63325383762611660801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.107 Γ— 10⁹⁸(99-digit number)
11072842402283216372…26650767525223321601
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 1584350

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 f59d350a89ea37c567ac59c03243cee0cb8362f4e593de500f266ecd2d2955e7

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 #1,584,350 on Chainz β†—
Circulating Supply:57,991,042 XPMΒ·at block #6,843,334 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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