XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,153,382

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/24/2019, 11:48:49 AM Β· Difficulty 11.3239 Β· 3,691,917 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e131cad218ecc88c3436ebc61038d52d4ca06cf940ffe3c386a5c3fa4d254a7b
View on Chainz β†—

Height

#3,153,382

Difficulty

11.323885

Transactions

1

Size

200 B

Version

2

Bits

0b52ea1f

Nonce

646,380,409

Timestamp

4/24/2019, 11:48:49 AM

Confirmations

3,691,917

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

837d00c1ccbda59523922bb6f1531f8e613478245a9ae53388ccfa049cc79eac
Transactions (1)
Coinbase837d00c1ccbda5…ccfa049cc79eac
1 in β†’ 1 out7.7900 XPM110 B
AbXwmGxD…4XXYP765
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.

8.741 Γ— 10⁹⁡(96-digit number)
87418361805475015085…52753045554874941441
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
8.741 Γ— 10⁹⁡(96-digit number)
87418361805475015085…52753045554874941441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.748 Γ— 10⁹⁢(97-digit number)
17483672361095003017…05506091109749882881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.496 Γ— 10⁹⁢(97-digit number)
34967344722190006034…11012182219499765761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.993 Γ— 10⁹⁢(97-digit number)
69934689444380012068…22024364438999531521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.398 Γ— 10⁹⁷(98-digit number)
13986937888876002413…44048728877999063041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.797 Γ— 10⁹⁷(98-digit number)
27973875777752004827…88097457755998126081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.594 Γ— 10⁹⁷(98-digit number)
55947751555504009654…76194915511996252161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.118 Γ— 10⁹⁸(99-digit number)
11189550311100801930…52389831023992504321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.237 Γ— 10⁹⁸(99-digit number)
22379100622201603861…04779662047985008641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.475 Γ— 10⁹⁸(99-digit number)
44758201244403207723…09559324095970017281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.951 Γ— 10⁹⁸(99-digit number)
89516402488806415447…19118648191940034561
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:58,006,831 XPMΒ·at block #6,845,298 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