XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,696,746

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/8/2018, 8:56:05 AM Β· Difficulty 11.6631 Β· 4,146,205 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
39273fb8763bdfc8060dc68fd062f05667b03db1d1c3202a7bc267e86c0eacc2
View on Chainz β†—

Height

#2,696,746

Difficulty

11.663121

Transactions

2

Size

574 B

Version

2

Bits

0ba9c24d

Nonce

1,773,382,743

Timestamp

6/8/2018, 8:56:05 AM

Confirmations

4,146,205

Mined by

⛏️ P2SHAZmZk4wBJszQg47TUR9KJA3D7Dzd46qS7c

Merkle Root

c2ca71618fb21be8f71b2f5fbfc6fe6bc13ea0572cc8b979e11582f8a119a615
Transactions (2)
Coinbase7f931fa8d9202f…f61c1a3e8312ad
1 in β†’ 1 out7.3500 XPM110 B
AZmZk4wB…zd46qS7c
c11df7fe403dc8…87a584be820ba8
2 in β†’ 2 out5.0123 XPM374 B
ATw23qLm…LfWAxVXEAX1aMNbv…uzy5PBqq
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.

1.797 Γ— 10⁹⁴(95-digit number)
17974661292972962946…96369826992264337921
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
1.797 Γ— 10⁹⁴(95-digit number)
17974661292972962946…96369826992264337921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.594 Γ— 10⁹⁴(95-digit number)
35949322585945925893…92739653984528675841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.189 Γ— 10⁹⁴(95-digit number)
71898645171891851787…85479307969057351681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.437 Γ— 10⁹⁡(96-digit number)
14379729034378370357…70958615938114703361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.875 Γ— 10⁹⁡(96-digit number)
28759458068756740715…41917231876229406721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.751 Γ— 10⁹⁡(96-digit number)
57518916137513481430…83834463752458813441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.150 Γ— 10⁹⁢(97-digit number)
11503783227502696286…67668927504917626881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.300 Γ— 10⁹⁢(97-digit number)
23007566455005392572…35337855009835253761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.601 Γ— 10⁹⁢(97-digit number)
46015132910010785144…70675710019670507521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.203 Γ— 10⁹⁢(97-digit number)
92030265820021570288…41351420039341015041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.840 Γ— 10⁹⁷(98-digit number)
18406053164004314057…82702840078682030081
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:57,987,960 XPMΒ·at block #6,842,950 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