XPM Prime Explorer symbol
XPMPrime Explorer

Block #86,471

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/28/2013, 4:05:08 AM Β· Difficulty 9.2884 Β· 6,723,105 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
be2f8f17c06d9553e536cd4a6fb0af0485148bd4a63d4542c434ac85255cd363
View on Chainz β†—

Height

#86,471

Difficulty

9.288417

Transactions

2

Size

982 B

Version

2

Bits

0949d5b4

Nonce

27

Timestamp

7/28/2013, 4:05:08 AM

Confirmations

6,723,105

Mined by

⛏️ P2SHAJz9V9LyDjeSNZ4NYpMs7mTFSYGCTyUhsC

Merkle Root

afa79072c4783c1e7e88eda401fdb8ccc48ff6383e6a49521f7d7fc4f6c343f0
Transactions (2)
Coinbase155b292d980c47…59c2db0f2cec6d
1 in β†’ 1 out11.5800 XPM110 B
AJz9V9Ly…GCTyUhsC
515d55ac175721…34267b0ae2b38c
5 in β†’ 1 out5851.9900 XPM783 B
AHUHdR12…b1vdLXJM
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.

9.178 Γ— 10⁹²(93-digit number)
91789829594556019199…54932376460702410881
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
9.178 Γ— 10⁹²(93-digit number)
91789829594556019199…54932376460702410881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.835 Γ— 10⁹³(94-digit number)
18357965918911203839…09864752921404821761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.671 Γ— 10⁹³(94-digit number)
36715931837822407679…19729505842809643521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.343 Γ— 10⁹³(94-digit number)
73431863675644815359…39459011685619287041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.468 Γ— 10⁹⁴(95-digit number)
14686372735128963071…78918023371238574081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.937 Γ— 10⁹⁴(95-digit number)
29372745470257926143…57836046742477148161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.874 Γ— 10⁹⁴(95-digit number)
58745490940515852287…15672093484954296321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.174 Γ— 10⁹⁡(96-digit number)
11749098188103170457…31344186969908592641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.349 Γ— 10⁹⁡(96-digit number)
23498196376206340914…62688373939817185281
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:57,720,685 XPMΒ·at block #6,809,575 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.
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