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Block #168,880

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/17/2013, 2:53:21 PM Β· Difficulty 9.8683 Β· 6,639,157 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
61081a8f777fa01d1cee7b67cd22574897068662b080e4a0e7e49dc05e8619dd
View on Chainz β†—

Height

#168,880

Difficulty

9.868290

Transactions

1

Size

203 B

Version

2

Bits

09de483f

Nonce

33,556,536

Timestamp

9/17/2013, 2:53:21 PM

Confirmations

6,639,157

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

6aeedd83551416e794023a09b0e716ff6e32c909658aa1b24cbc363d27e3ba05
Transactions (1)
Coinbase6aeedd83551416…bc363d27e3ba05
1 in β†’ 1 out10.2500 XPM112 B
AcLBm5Z9…S683d7c3
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.

2.848 Γ— 10⁹⁢(97-digit number)
28488034442057259466…99081067179069296001
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
2.848 Γ— 10⁹⁢(97-digit number)
28488034442057259466…99081067179069296001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.697 Γ— 10⁹⁢(97-digit number)
56976068884114518932…98162134358138592001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.139 Γ— 10⁹⁷(98-digit number)
11395213776822903786…96324268716277184001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.279 Γ— 10⁹⁷(98-digit number)
22790427553645807572…92648537432554368001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.558 Γ— 10⁹⁷(98-digit number)
45580855107291615145…85297074865108736001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.116 Γ— 10⁹⁷(98-digit number)
91161710214583230291…70594149730217472001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.823 Γ— 10⁹⁸(99-digit number)
18232342042916646058…41188299460434944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.646 Γ— 10⁹⁸(99-digit number)
36464684085833292116…82376598920869888001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.292 Γ— 10⁹⁸(99-digit number)
72929368171666584233…64753197841739776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.458 Γ— 10⁹⁹(100-digit number)
14585873634333316846…29506395683479552001
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:57,708,341 XPMΒ·at block #6,808,036 Β· updates every 60s
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