XPM Prime Explorer symbol
XPMPrime Explorer

Block #162,358

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/13/2013, 6:30:55 AM Β· Difficulty 9.8611 Β· 6,655,677 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7804b57cbb0a3761196c655d8b0656e1ed905c26f1af9be5eaf49ccda691790b
View on Chainz β†—

Height

#162,358

Difficulty

9.861068

Transactions

2

Size

391 B

Version

2

Bits

09dc6efc

Nonce

185,157

Timestamp

9/13/2013, 6:30:55 AM

Confirmations

6,655,677

Mined by

⛏️ P2SHAaT9ZWXgbP8qCKba99Ysd5nxsG2aZTQ3Wx

Merkle Root

06be0938f0fe0c648f37b794fd7f34f2c0fe8731e4ca373ec87c4e6c9501670b
Transactions (2)
Coinbaseed7bdfc8d9b598…554e4481f4c2c7
1 in β†’ 1 out10.2800 XPM109 B
AaT9ZWXg…2aZTQ3Wx
6bc753d8f1bb67…f4b8fd3e184ef5
1 in β†’ 2 out10.2600 XPM192 B
AQyVDppr…6yVhub9rAFz9fXym…wh4UqpkL
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.

2.487 Γ— 10⁹⁴(95-digit number)
24879113024700221921…25116724666903125441
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
2.487 Γ— 10⁹⁴(95-digit number)
24879113024700221921…25116724666903125441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.975 Γ— 10⁹⁴(95-digit number)
49758226049400443842…50233449333806250881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.951 Γ— 10⁹⁴(95-digit number)
99516452098800887684…00466898667612501761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.990 Γ— 10⁹⁡(96-digit number)
19903290419760177536…00933797335225003521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.980 Γ— 10⁹⁡(96-digit number)
39806580839520355073…01867594670450007041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.961 Γ— 10⁹⁡(96-digit number)
79613161679040710147…03735189340900014081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.592 Γ— 10⁹⁢(97-digit number)
15922632335808142029…07470378681800028161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.184 Γ— 10⁹⁢(97-digit number)
31845264671616284058…14940757363600056321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.369 Γ— 10⁹⁢(97-digit number)
63690529343232568117…29881514727200112641
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,788,349 XPMΒ·at block #6,818,034 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