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Home/Chain Registry/Block #1,715,458

Block #1,715,458

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/13/2016, 3:29:15 PM Β· Difficulty 10.6576 Β· 5,115,882 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
24cfa0a4f9e9b0a80e2b592dde1386e7b53c866304b46997e7d65e114fff1afc
View on Chainz β†—

Difficulty

10.657571

Transactions

1

Size

199 B

Version

2

Bits

0aa85696

Nonce

1,422,603,902

Timestamp

8/13/2016, 3:29:15 PM

Confirmations

5,115,882

Merkle Root

c8903246c39c1c4d4cd8347cf84ffeb69ec320bcdb247200847fa2ac13ff980f
Transactions (1)
Coinbasec8903246c39c1c…7fa2ac13ff980f
1 in β†’ 1 out8.7900 XPM109 B
ANbmN9sc…T8XCLDeo
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.

6.789 Γ— 10⁹⁡(96-digit number)
67894660590778448187…72927544709196314880
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
6.789 Γ— 10⁹⁡(96-digit number)
67894660590778448187…72927544709196314881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.357 Γ— 10⁹⁢(97-digit number)
13578932118155689637…45855089418392629761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.715 Γ— 10⁹⁢(97-digit number)
27157864236311379274…91710178836785259521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.431 Γ— 10⁹⁢(97-digit number)
54315728472622758549…83420357673570519041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.086 Γ— 10⁹⁷(98-digit number)
10863145694524551709…66840715347141038081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.172 Γ— 10⁹⁷(98-digit number)
21726291389049103419…33681430694282076161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.345 Γ— 10⁹⁷(98-digit number)
43452582778098206839…67362861388564152321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.690 Γ— 10⁹⁷(98-digit number)
86905165556196413679…34725722777128304641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.738 Γ— 10⁹⁸(99-digit number)
17381033111239282735…69451445554256609281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.476 Γ— 10⁹⁸(99-digit number)
34762066222478565471…38902891108513218561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.952 Γ— 10⁹⁸(99-digit number)
69524132444957130943…77805782217026437121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 1715458

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 24cfa0a4f9e9b0a80e2b592dde1386e7b53c866304b46997e7d65e114fff1afc

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 #1,715,458 on Chainz β†—
Circulating Supply:57,894,873 XPMΒ·at block #6,831,339 Β· updates every 60s
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