XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,585,718

Block #1,585,718

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/15/2016, 2:05:53 PM Β· Difficulty 10.6482 Β· 5,232,126 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
00392e0a313c68c3473268ac63bdf98cd4090dbfb73f2656cc2c0b2852940c59
View on Chainz β†—

Difficulty

10.648171

Transactions

1

Size

243 B

Version

2

Bits

0aa5ee90

Nonce

152,210,809

Timestamp

5/15/2016, 2:05:53 PM

Confirmations

5,232,126

Merkle Root

fbc1131b7706075a0ab99a1eb0e21a234d94fd87fdb2e08d9bbe5652c60ad1ec
Transactions (1)
Coinbasefbc1131b770607…be5652c60ad1ec
1 in β†’ 2 out8.8100 XPM152 B
AXZf8xqq…hQwCQgXtALPu3s2c…EJXLjVFh
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.

4.695 Γ— 10⁹⁢(97-digit number)
46955897483840795205…05994717617214051520
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
4.695 Γ— 10⁹⁢(97-digit number)
46955897483840795205…05994717617214051521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.391 Γ— 10⁹⁢(97-digit number)
93911794967681590410…11989435234428103041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.878 Γ— 10⁹⁷(98-digit number)
18782358993536318082…23978870468856206081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.756 Γ— 10⁹⁷(98-digit number)
37564717987072636164…47957740937712412161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.512 Γ— 10⁹⁷(98-digit number)
75129435974145272328…95915481875424824321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.502 Γ— 10⁹⁸(99-digit number)
15025887194829054465…91830963750849648641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.005 Γ— 10⁹⁸(99-digit number)
30051774389658108931…83661927501699297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.010 Γ— 10⁹⁸(99-digit number)
60103548779316217863…67323855003398594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.202 Γ— 10⁹⁹(100-digit number)
12020709755863243572…34647710006797189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.404 Γ— 10⁹⁹(100-digit number)
24041419511726487145…69295420013594378241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.808 Γ— 10⁹⁹(100-digit number)
48082839023452974290…38590840027188756481
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 1585718

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 00392e0a313c68c3473268ac63bdf98cd4090dbfb73f2656cc2c0b2852940c59

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 #1,585,718 on Chainz β†—
Circulating Supply:57,786,817 XPMΒ·at block #6,817,843 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