XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,697,793

Block #1,697,793

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/1/2016, 5:05:49 AM Β· Difficulty 10.6727 Β· 5,143,655 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
36fdfe61b70333cb44a92f5dd3ce68f4ac4d6ff8839b513ea917b44aab37c946
View on Chainz β†—

Difficulty

10.672699

Transactions

1

Size

243 B

Version

2

Bits

0aac35fd

Nonce

858,762,279

Timestamp

8/1/2016, 5:05:49 AM

Confirmations

5,143,655

Merkle Root

adcc005c27289af35a363136e55fb87f7f9b426a4338db68a7fb6efe30174656
Transactions (1)
Coinbaseadcc005c27289a…fb6efe30174656
1 in β†’ 2 out8.7700 XPM152 B
AGkY5Euz…5TxsxHeGALPu3s2c…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.

2.560 Γ— 10⁹⁷(98-digit number)
25601043535790745914…73236873058470013440
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.560 Γ— 10⁹⁷(98-digit number)
25601043535790745914…73236873058470013439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.120 Γ— 10⁹⁷(98-digit number)
51202087071581491829…46473746116940026879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.024 Γ— 10⁹⁸(99-digit number)
10240417414316298365…92947492233880053759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.048 Γ— 10⁹⁸(99-digit number)
20480834828632596731…85894984467760107519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.096 Γ— 10⁹⁸(99-digit number)
40961669657265193463…71789968935520215039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.192 Γ— 10⁹⁸(99-digit number)
81923339314530386926…43579937871040430079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.638 Γ— 10⁹⁹(100-digit number)
16384667862906077385…87159875742080860159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.276 Γ— 10⁹⁹(100-digit number)
32769335725812154770…74319751484161720319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.553 Γ— 10⁹⁹(100-digit number)
65538671451624309541…48639502968323440639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.310 Γ— 10¹⁰⁰(101-digit number)
13107734290324861908…97279005936646881279
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 1697793

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 36fdfe61b70333cb44a92f5dd3ce68f4ac4d6ff8839b513ea917b44aab37c946

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 #1,697,793 on Chainz β†—
Circulating Supply:57,975,963 XPMΒ·at block #6,841,447 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