XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,856,638

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/27/2018, 4:08:23 AM Β· Difficulty 11.6903 Β· 3,985,137 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6729832f6e200b891817340a8ac8fa3479c040333da2b50bfc21285361c86dad
View on Chainz β†—

Height

#2,856,638

Difficulty

11.690309

Transactions

1

Size

201 B

Version

2

Bits

0bb0b81c

Nonce

81,792,030

Timestamp

9/27/2018, 4:08:23 AM

Confirmations

3,985,137

Mined by

⛏️ P2SHAKv1GgJFuuZJhwF4dgZ3RkF2wKR2nLwmcJ

Merkle Root

501cf48b3d13dd4f9aff820a8228c92ab599b5268826dd1937b2ba38f6911e19
Transactions (1)
Coinbase501cf48b3d13dd…b2ba38f6911e19
1 in β†’ 1 out7.3000 XPM110 B
AKv1GgJF…R2nLwmcJ
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.

1.477 Γ— 10⁹⁢(97-digit number)
14776500620449419519…55305746147599831041
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
1.477 Γ— 10⁹⁢(97-digit number)
14776500620449419519…55305746147599831041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.955 Γ— 10⁹⁢(97-digit number)
29553001240898839039…10611492295199662081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.910 Γ— 10⁹⁢(97-digit number)
59106002481797678079…21222984590399324161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.182 Γ— 10⁹⁷(98-digit number)
11821200496359535615…42445969180798648321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.364 Γ— 10⁹⁷(98-digit number)
23642400992719071231…84891938361597296641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.728 Γ— 10⁹⁷(98-digit number)
47284801985438142463…69783876723194593281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.456 Γ— 10⁹⁷(98-digit number)
94569603970876284927…39567753446389186561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.891 Γ— 10⁹⁸(99-digit number)
18913920794175256985…79135506892778373121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.782 Γ— 10⁹⁸(99-digit number)
37827841588350513970…58271013785556746241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.565 Γ— 10⁹⁸(99-digit number)
75655683176701027941…16542027571113492481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.513 Γ— 10⁹⁹(100-digit number)
15131136635340205588…33084055142226984961
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:57,978,577 XPMΒ·at block #6,841,774 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