XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,613,788

Block #1,613,788

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2016, 1:44:30 PM Β· Difficulty 10.5965 Β· 5,228,187 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
107511602eadcf65fdd410c9a19535cc62267c4d3f372f623a589c8e7ab33334
View on Chainz β†—

Difficulty

10.596501

Transactions

1

Size

199 B

Version

2

Bits

0a98b451

Nonce

825,980,593

Timestamp

6/4/2016, 1:44:30 PM

Confirmations

5,228,187

Merkle Root

d2af0cf11bc48640e19df396a7cea8be597d59afff6d763168087ff4008324a7
Transactions (1)
Coinbased2af0cf11bc486…087ff4008324a7
1 in β†’ 1 out8.8900 XPM109 B
AHuuPZtS…8wu3awZo
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.

4.864 Γ— 10⁹⁴(95-digit number)
48647504066960822076…93364162998177963600
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
4.864 Γ— 10⁹⁴(95-digit number)
48647504066960822076…93364162998177963601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.729 Γ— 10⁹⁴(95-digit number)
97295008133921644153…86728325996355927201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.945 Γ— 10⁹⁡(96-digit number)
19459001626784328830…73456651992711854401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.891 Γ— 10⁹⁡(96-digit number)
38918003253568657661…46913303985423708801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.783 Γ— 10⁹⁡(96-digit number)
77836006507137315322…93826607970847417601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.556 Γ— 10⁹⁢(97-digit number)
15567201301427463064…87653215941694835201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.113 Γ— 10⁹⁢(97-digit number)
31134402602854926129…75306431883389670401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.226 Γ— 10⁹⁢(97-digit number)
62268805205709852258…50612863766779340801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.245 Γ— 10⁹⁷(98-digit number)
12453761041141970451…01225727533558681601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.490 Γ— 10⁹⁷(98-digit number)
24907522082283940903…02451455067117363201
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 1613788

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 107511602eadcf65fdd410c9a19535cc62267c4d3f372f623a589c8e7ab33334

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 #1,613,788 on Chainz β†—
Circulating Supply:57,980,184 XPMΒ·at block #6,841,974 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