XPM Prime Explorer symbol
XPMPrime Explorer

Block #247,738

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/6/2013, 11:01:33 PM Β· Difficulty 9.9652 Β· 6,579,223 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7e6083a6330708f193bf8be70b1cef7adb83e05d5faeaf1dca8d9de4a2b8c9b7
View on Chainz β†—

Height

#247,738

Difficulty

9.965180

Transactions

1

Size

208 B

Version

2

Bits

09f71608

Nonce

428,940

Timestamp

11/6/2013, 11:01:33 PM

Confirmations

6,579,223

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

f5dbada29300f168d07cad7847f1590a71ba67b9f193081c3bc2e3b09b23a0ac
Transactions (1)
Coinbasef5dbada29300f1…c2e3b09b23a0ac
1 in β†’ 1 out10.0500 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.280 Γ— 10⁹⁹(100-digit number)
42808519601421210646…77307198334171281629
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
4.280 Γ— 10⁹⁹(100-digit number)
42808519601421210646…77307198334171281629
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.561 Γ— 10⁹⁹(100-digit number)
85617039202842421292…54614396668342563259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.712 Γ— 10¹⁰⁰(101-digit number)
17123407840568484258…09228793336685126519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.424 Γ— 10¹⁰⁰(101-digit number)
34246815681136968517…18457586673370253039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.849 Γ— 10¹⁰⁰(101-digit number)
68493631362273937034…36915173346740506079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.369 Γ— 10¹⁰¹(102-digit number)
13698726272454787406…73830346693481012159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.739 Γ— 10¹⁰¹(102-digit number)
27397452544909574813…47660693386962024319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.479 Γ— 10¹⁰¹(102-digit number)
54794905089819149627…95321386773924048639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.095 Γ— 10¹⁰²(103-digit number)
10958981017963829925…90642773547848097279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.191 Γ— 10¹⁰²(103-digit number)
21917962035927659850…81285547095696194559
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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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, …
Cross-reference on Chainz Explorer
Circulating Supply:57,859,864 XPMΒ·at block #6,826,960 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