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Home/Chain Registry/Block #1,719,152

Block #1,719,152

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/16/2016, 1:43:08 AM Β· Difficulty 10.6710 Β· 5,081,753 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e5a5065134924cd0e24edf11aa995ce418f861d95b42e4e7bdd5d280f49f17e6
View on Chainz β†—

Difficulty

10.671040

Transactions

1

Size

200 B

Version

2

Bits

0aabc941

Nonce

1,645,139,255

Timestamp

8/16/2016, 1:43:08 AM

Confirmations

5,081,753

Merkle Root

6d699ebf5b9e372bb3d866ecf60dc31c37564f1135458b36e01c6570b4b9ebd1
Transactions (1)
Coinbase6d699ebf5b9e37…1c6570b4b9ebd1
1 in β†’ 1 out8.7700 XPM110 B
AbwVBULB…BLs9JVbi
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.

4.029 Γ— 10⁹⁡(96-digit number)
40290300265724787592…93023638131242712960
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
4.029 Γ— 10⁹⁡(96-digit number)
40290300265724787592…93023638131242712961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.058 Γ— 10⁹⁡(96-digit number)
80580600531449575184…86047276262485425921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.611 Γ— 10⁹⁢(97-digit number)
16116120106289915036…72094552524970851841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.223 Γ— 10⁹⁢(97-digit number)
32232240212579830073…44189105049941703681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.446 Γ— 10⁹⁢(97-digit number)
64464480425159660147…88378210099883407361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.289 Γ— 10⁹⁷(98-digit number)
12892896085031932029…76756420199766814721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.578 Γ— 10⁹⁷(98-digit number)
25785792170063864059…53512840399533629441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.157 Γ— 10⁹⁷(98-digit number)
51571584340127728118…07025680799067258881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.031 Γ— 10⁹⁸(99-digit number)
10314316868025545623…14051361598134517761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.062 Γ— 10⁹⁸(99-digit number)
20628633736051091247…28102723196269035521
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 1719152

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 e5a5065134924cd0e24edf11aa995ce418f861d95b42e4e7bdd5d280f49f17e6

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 #1,719,152 on Chainz β†—
Circulating Supply:57,651,300 XPMΒ·at block #6,800,904 Β· updates every 60s
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