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Block #80,517

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/24/2013, 5:15:13 AM Β· Difficulty 9.2499 Β· 6,714,303 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c079e4fd7a99a2b094bd0055e27790a897da5bcacc936951b86be32f5cbaa36
View on Chainz β†—

Height

#80,517

Difficulty

9.249892

Transactions

2

Size

539 B

Version

2

Bits

093ff8ed

Nonce

655,096

Timestamp

7/24/2013, 5:15:13 AM

Confirmations

6,714,303

Mined by

⛏️ P2SHAcnSJJFemB4F2prjX4RYa3fGuJ93jjyWm1

Merkle Root

08a582acc9a27f4d69c1e7282f6d7dbd04f478150099e668eba41fd07bfaa254
Transactions (2)
Coinbase0c96db560c18d1…2929217c3bfe83
1 in β†’ 1 out11.6800 XPM109 B
AcnSJJFe…93jjyWm1
8a3e6af791821c…a6b38cf09f951a
2 in β†’ 1 out99.9000 XPM339 B
AYoEHY4g…ALEhq74r
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.

1.690 Γ— 10⁹⁸(99-digit number)
16902456972913436777…98156809350372485381
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
1.690 Γ— 10⁹⁸(99-digit number)
16902456972913436777…98156809350372485381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.380 Γ— 10⁹⁸(99-digit number)
33804913945826873555…96313618700744970761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.760 Γ— 10⁹⁸(99-digit number)
67609827891653747111…92627237401489941521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.352 Γ— 10⁹⁹(100-digit number)
13521965578330749422…85254474802979883041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.704 Γ— 10⁹⁹(100-digit number)
27043931156661498844…70508949605959766081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.408 Γ— 10⁹⁹(100-digit number)
54087862313322997688…41017899211919532161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.081 Γ— 10¹⁰⁰(101-digit number)
10817572462664599537…82035798423839064321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.163 Γ— 10¹⁰⁰(101-digit number)
21635144925329199075…64071596847678128641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.327 Γ— 10¹⁰⁰(101-digit number)
43270289850658398151…28143193695356257281
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:57,602,608 XPMΒ·at block #6,794,819 Β· updates every 60s
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