XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,691,260

Block #1,691,260

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/27/2016, 11:50:48 AM Β· Difficulty 10.6891 Β· 5,141,355 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
06ddb982b7d58557fb1730968e14a87fdda536b597ec5eb05c9b79de1ed587a7
View on Chainz β†—

Difficulty

10.689134

Transactions

1

Size

199 B

Version

2

Bits

0ab06b18

Nonce

880,542,933

Timestamp

7/27/2016, 11:50:48 AM

Confirmations

5,141,355

Merkle Root

6da627f8f1602ce50021c7e42c4536b89794732dc29f24c6ca5032816a970bad
Transactions (1)
Coinbase6da627f8f1602c…5032816a970bad
1 in β†’ 1 out8.7400 XPM109 B
ARBcBEew…iAMg4hAN
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.

3.668 Γ— 10⁹⁡(96-digit number)
36686496230411152374…20017808583122864640
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
3.668 Γ— 10⁹⁡(96-digit number)
36686496230411152374…20017808583122864641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.337 Γ— 10⁹⁡(96-digit number)
73372992460822304748…40035617166245729281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.467 Γ— 10⁹⁢(97-digit number)
14674598492164460949…80071234332491458561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.934 Γ— 10⁹⁢(97-digit number)
29349196984328921899…60142468664982917121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.869 Γ— 10⁹⁢(97-digit number)
58698393968657843798…20284937329965834241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.173 Γ— 10⁹⁷(98-digit number)
11739678793731568759…40569874659931668481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.347 Γ— 10⁹⁷(98-digit number)
23479357587463137519…81139749319863336961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.695 Γ— 10⁹⁷(98-digit number)
46958715174926275038…62279498639726673921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.391 Γ— 10⁹⁷(98-digit number)
93917430349852550077…24558997279453347841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.878 Γ— 10⁹⁸(99-digit number)
18783486069970510015…49117994558906695681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.756 Γ— 10⁹⁸(99-digit number)
37566972139941020031…98235989117813391361
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 1691260

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 06ddb982b7d58557fb1730968e14a87fdda536b597ec5eb05c9b79de1ed587a7

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 #1,691,260 on Chainz β†—
Circulating Supply:57,905,066 XPMΒ·at block #6,832,614 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy