XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,009,194

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/14/2019, 11:10:20 AM Β· Difficulty 11.2023 Β· 3,831,885 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8c11b1f28ee0edd4019b11764aa60ab4e3ab9a016129b871caca45e8d072011a
View on Chainz β†—

Height

#3,009,194

Difficulty

11.202263

Transactions

1

Size

200 B

Version

2

Bits

0b33c77b

Nonce

222,793,943

Timestamp

1/14/2019, 11:10:20 AM

Confirmations

3,831,885

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

1df264b7db593a41342362c24e6076f4ae0092cfdb4a44b6c56277f4942bf80d
Transactions (1)
Coinbase1df264b7db593a…6277f4942bf80d
1 in β†’ 1 out7.9600 XPM110 B
AUMQRepm…tAfKmdW1
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.

2.212 Γ— 10⁹⁴(95-digit number)
22122673836087281348…09170606835804672721
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
2.212 Γ— 10⁹⁴(95-digit number)
22122673836087281348…09170606835804672721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.424 Γ— 10⁹⁴(95-digit number)
44245347672174562696…18341213671609345441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.849 Γ— 10⁹⁴(95-digit number)
88490695344349125393…36682427343218690881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.769 Γ— 10⁹⁡(96-digit number)
17698139068869825078…73364854686437381761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.539 Γ— 10⁹⁡(96-digit number)
35396278137739650157…46729709372874763521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.079 Γ— 10⁹⁡(96-digit number)
70792556275479300315…93459418745749527041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.415 Γ— 10⁹⁢(97-digit number)
14158511255095860063…86918837491499054081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.831 Γ— 10⁹⁢(97-digit number)
28317022510191720126…73837674982998108161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.663 Γ— 10⁹⁢(97-digit number)
56634045020383440252…47675349965996216321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.132 Γ— 10⁹⁷(98-digit number)
11326809004076688050…95350699931992432641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.265 Γ— 10⁹⁷(98-digit number)
22653618008153376100…90701399863984865281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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, …
Cross-reference on Chainz Explorer
Circulating Supply:57,972,995 XPMΒ·at block #6,841,078 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