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Block #1,613,850

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2016, 2:59:19 PM Β· Difficulty 10.5953 Β· 5,229,155 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
80e36c75d67e8211e3aeebdf3108b02a92acf313c88bb4ab4a360d69e87cc88e
View on Chainz β†—

Difficulty

10.595295

Transactions

1

Size

200 B

Version

2

Bits

0a98653c

Nonce

298,930,982

Timestamp

6/4/2016, 2:59:19 PM

Confirmations

5,229,155

Merkle Root

4655501987feb228764b21247c93e0f1126e1ab7f196cdcf0297bbd7e03246a5
Transactions (1)
Coinbase4655501987feb2…97bbd7e03246a5
1 in β†’ 1 out8.8900 XPM110 B
AVbezduG…hnnLECW6
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.

6.333 Γ— 10⁹⁴(95-digit number)
63335863923841147105…67334191709767604000
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
6.333 Γ— 10⁹⁴(95-digit number)
63335863923841147105…67334191709767604001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.266 Γ— 10⁹⁡(96-digit number)
12667172784768229421…34668383419535208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.533 Γ— 10⁹⁡(96-digit number)
25334345569536458842…69336766839070416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.066 Γ— 10⁹⁡(96-digit number)
50668691139072917684…38673533678140832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.013 Γ— 10⁹⁢(97-digit number)
10133738227814583536…77347067356281664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.026 Γ— 10⁹⁢(97-digit number)
20267476455629167073…54694134712563328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.053 Γ— 10⁹⁢(97-digit number)
40534952911258334147…09388269425126656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.106 Γ— 10⁹⁢(97-digit number)
81069905822516668295…18776538850253312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.621 Γ— 10⁹⁷(98-digit number)
16213981164503333659…37553077700506624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.242 Γ— 10⁹⁷(98-digit number)
32427962329006667318…75106155401013248001
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 1613850

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 80e36c75d67e8211e3aeebdf3108b02a92acf313c88bb4ab4a360d69e87cc88e

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 #1,613,850 on Chainz β†—
Circulating Supply:57,988,397 XPMΒ·at block #6,843,004 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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