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Block #82,914

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/25/2013, 6:34:57 PM Β· Difficulty 9.2730 Β· 6,744,186 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
882ce25d428b1dbf002b328ea2058236e6ad906f3062562d969ce1ed4c1d7acf
View on Chainz β†—

Height

#82,914

Difficulty

9.272963

Transactions

2

Size

355 B

Version

2

Bits

0945e0ec

Nonce

226,735

Timestamp

7/25/2013, 6:34:57 PM

Confirmations

6,744,186

Mined by

⛏️ P2SHAdQLBC3YmFVkSxZqATf2fhfBqr1tJ87FgZ

Merkle Root

27a7640484831a87798a177743ca06483b4504d789581d7e0b51c18a61fc6bd3
Transactions (2)
Coinbase5191b8714a63f6…7e5fb8bd2812b5
1 in β†’ 1 out11.6200 XPM109 B
AdQLBC3Y…1tJ87FgZ
7cefcf67f3c947…a5a7b00ce1dee5
1 in β†’ 1 out11.6800 XPM158 B
AbhWjNtr…ZGT63E3Y
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.

1.314 Γ— 10⁹⁰(91-digit number)
13146597084687479172…65940078527347489221
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
1.314 Γ— 10⁹⁰(91-digit number)
13146597084687479172…65940078527347489221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.629 Γ— 10⁹⁰(91-digit number)
26293194169374958344…31880157054694978441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.258 Γ— 10⁹⁰(91-digit number)
52586388338749916688…63760314109389956881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.051 Γ— 10⁹¹(92-digit number)
10517277667749983337…27520628218779913761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.103 Γ— 10⁹¹(92-digit number)
21034555335499966675…55041256437559827521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.206 Γ— 10⁹¹(92-digit number)
42069110670999933350…10082512875119655041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.413 Γ— 10⁹¹(92-digit number)
84138221341999866701…20165025750239310081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.682 Γ— 10⁹²(93-digit number)
16827644268399973340…40330051500478620161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.365 Γ— 10⁹²(93-digit number)
33655288536799946680…80660103000957240321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.731 Γ— 10⁹²(93-digit number)
67310577073599893361…61320206001914480641
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,860,977 XPMΒ·at block #6,827,099 Β· updates every 60s
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