XPM Prime Explorer symbol
XPMPrime Explorer

Block #214,311

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/17/2013, 10:17:36 AM Β· Difficulty 9.9228 Β· 6,596,364 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e3d15f41ea54d8d612106080be568cc2110cd2f48e1c65ab4c89c33d70051fc9
View on Chainz β†—

Height

#214,311

Difficulty

9.922806

Transactions

1

Size

199 B

Version

2

Bits

09ec3d03

Nonce

58,631

Timestamp

10/17/2013, 10:17:36 AM

Confirmations

6,596,364

Mined by

⛏️ P2SHAMDDjcKidTR7e5DmAbqsZdJTifMcrtk5gH

Merkle Root

98a91a2d4bf737b15f89269864edbf1364284b4f5cb59611f07369148d61a4a2
Transactions (1)
Coinbase98a91a2d4bf737…7369148d61a4a2
1 in β†’ 1 out10.1400 XPM109 B
AMDDjcKi…Mcrtk5gH
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.

3.093 Γ— 10⁹⁴(95-digit number)
30934684522961523376…11676564977016075039
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
3.093 Γ— 10⁹⁴(95-digit number)
30934684522961523376…11676564977016075039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.186 Γ— 10⁹⁴(95-digit number)
61869369045923046752…23353129954032150079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.237 Γ— 10⁹⁡(96-digit number)
12373873809184609350…46706259908064300159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.474 Γ— 10⁹⁡(96-digit number)
24747747618369218701…93412519816128600319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.949 Γ— 10⁹⁡(96-digit number)
49495495236738437402…86825039632257200639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.899 Γ— 10⁹⁡(96-digit number)
98990990473476874804…73650079264514401279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.979 Γ— 10⁹⁢(97-digit number)
19798198094695374960…47300158529028802559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.959 Γ— 10⁹⁢(97-digit number)
39596396189390749921…94600317058057605119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.919 Γ— 10⁹⁢(97-digit number)
79192792378781499843…89200634116115210239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.583 Γ— 10⁹⁷(98-digit number)
15838558475756299968…78401268232230420479
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:57,729,491 XPMΒ·at block #6,810,674 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.
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