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Home/Chain Registry/Block #1,643,936

Block #1,643,936

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/24/2016, 7:50:55 PM Β· Difficulty 10.6691 Β· 5,180,875 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d325a375711c9f65e7a2ca25eebe93398c163edb8b87384d530457a68cf3a77e
View on Chainz β†—

Difficulty

10.669108

Transactions

1

Size

199 B

Version

2

Bits

0aab4aa4

Nonce

1,542,757,977

Timestamp

6/24/2016, 7:50:55 PM

Confirmations

5,180,875

Merkle Root

037263d1d7d8e38cc6f52203b1559e4bfd4e708c83a682b0f1c7e28701a05014
Transactions (1)
Coinbase037263d1d7d8e3…c7e28701a05014
1 in β†’ 1 out8.7700 XPM109 B
AS6NN7Lw…c1sUfQpX
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.

7.625 Γ— 10⁹⁴(95-digit number)
76251974378458433365…16166556778615320000
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
7.625 Γ— 10⁹⁴(95-digit number)
76251974378458433365…16166556778615320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.525 Γ— 10⁹⁡(96-digit number)
15250394875691686673…32333113557230640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.050 Γ— 10⁹⁡(96-digit number)
30500789751383373346…64666227114461280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.100 Γ— 10⁹⁡(96-digit number)
61001579502766746692…29332454228922560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.220 Γ— 10⁹⁢(97-digit number)
12200315900553349338…58664908457845120001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.440 Γ— 10⁹⁢(97-digit number)
24400631801106698676…17329816915690240001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.880 Γ— 10⁹⁢(97-digit number)
48801263602213397353…34659633831380480001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.760 Γ— 10⁹⁢(97-digit number)
97602527204426794707…69319267662760960001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.952 Γ— 10⁹⁷(98-digit number)
19520505440885358941…38638535325521920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.904 Γ— 10⁹⁷(98-digit number)
39041010881770717883…77277070651043840001
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 1643936

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 d325a375711c9f65e7a2ca25eebe93398c163edb8b87384d530457a68cf3a77e

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 #1,643,936 on Chainz β†—
Circulating Supply:57,842,565 XPMΒ·at block #6,824,810 Β· updates every 60s
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