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Home/Chain Registry/Block #2,131,044

Block #2,131,044

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2017, 8:02:10 PM Β· Difficulty 10.9103 Β· 4,695,934 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d572a474fd21ce6942dd3c82fb46d6cef6a5a75d41183bcc17b1c4a2f7c5d96d
View on Chainz β†—

Difficulty

10.910258

Transactions

2

Size

1.10 KB

Version

2

Bits

0ae906b0

Nonce

1,107,464,160

Timestamp

5/24/2017, 8:02:10 PM

Confirmations

4,695,934

Merkle Root

19d6100cfbb984d8a81d127ec3d2e0ec836054ae04ab0444822ca184f9820132
Transactions (2)
Coinbase12c91a413657c4…56624e6485dae2
1 in β†’ 1 out8.4200 XPM109 B
AMFXHoXF…JeWxraNf
e0e7eef6cf7322…a0f98e4be8ef7b
6 in β†’ 1 out26.2828 XPM927 B
Aarnxjc9…QbpXFbC9
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.

8.494 Γ— 10⁹³(94-digit number)
84941942576063724510…26779191918529064860
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
8.494 Γ— 10⁹³(94-digit number)
84941942576063724510…26779191918529064861
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.698 Γ— 10⁹⁴(95-digit number)
16988388515212744902…53558383837058129721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.397 Γ— 10⁹⁴(95-digit number)
33976777030425489804…07116767674116259441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.795 Γ— 10⁹⁴(95-digit number)
67953554060850979608…14233535348232518881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.359 Γ— 10⁹⁡(96-digit number)
13590710812170195921…28467070696465037761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.718 Γ— 10⁹⁡(96-digit number)
27181421624340391843…56934141392930075521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.436 Γ— 10⁹⁡(96-digit number)
54362843248680783686…13868282785860151041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.087 Γ— 10⁹⁢(97-digit number)
10872568649736156737…27736565571720302081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.174 Γ— 10⁹⁢(97-digit number)
21745137299472313474…55473131143440604161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.349 Γ— 10⁹⁢(97-digit number)
43490274598944626949…10946262286881208321
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 2131044

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 d572a474fd21ce6942dd3c82fb46d6cef6a5a75d41183bcc17b1c4a2f7c5d96d

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 #2,131,044 on Chainz β†—
Circulating Supply:57,859,998 XPMΒ·at block #6,826,977 Β· updates every 60s
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