XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #124,662

Block #124,662

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/19/2013, 6:54:33 PM Β· Difficulty 9.7724 Β· 6,702,268 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e2eba1280b5342ea8151fda0247a28bfaa7a21de13ff07b29f6772b0c186215c
View on Chainz β†—

Height

#124,662

Difficulty

9.772393

Transactions

1

Size

200 B

Version

2

Bits

09c5bb88

Nonce

925,271

Timestamp

8/19/2013, 6:54:33 PM

Confirmations

6,702,268

Merkle Root

9ea486371d4fd2d70f3ea340335228ea540f5ea9f34510ddc7c7f3dbcb9c0e99
Transactions (1)
Coinbase9ea486371d4fd2…c7f3dbcb9c0e99
1 in β†’ 1 out10.4600 XPM109 B
AcMYZ4y2…SA8KujQk
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.

3.012 Γ— 10⁹⁢(97-digit number)
30120283088077548679…60520936426778974280
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
3.012 Γ— 10⁹⁢(97-digit number)
30120283088077548679…60520936426778974281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.024 Γ— 10⁹⁢(97-digit number)
60240566176155097358…21041872853557948561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.204 Γ— 10⁹⁷(98-digit number)
12048113235231019471…42083745707115897121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.409 Γ— 10⁹⁷(98-digit number)
24096226470462038943…84167491414231794241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.819 Γ— 10⁹⁷(98-digit number)
48192452940924077886…68334982828463588481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.638 Γ— 10⁹⁷(98-digit number)
96384905881848155773…36669965656927176961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.927 Γ— 10⁹⁸(99-digit number)
19276981176369631154…73339931313854353921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.855 Γ— 10⁹⁸(99-digit number)
38553962352739262309…46679862627708707841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.710 Γ— 10⁹⁸(99-digit number)
77107924705478524618…93359725255417415681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.542 Γ— 10⁹⁹(100-digit number)
15421584941095704923…86719450510834831361
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 124662

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 e2eba1280b5342ea8151fda0247a28bfaa7a21de13ff07b29f6772b0c186215c

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 #124,662 on Chainz β†—
Circulating Supply:57,859,612 XPMΒ·at block #6,826,929 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