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Block #1,079,117

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/28/2015, 12:02:06 AM Β· Difficulty 10.7644 Β· 5,724,161 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6e56cc8ba13958caadf4c39f0be35f3f1f3a184bda0c524f74e9d79394e38899
View on Chainz β†—

Height

#1,079,117

Difficulty

10.764408

Transactions

1

Size

201 B

Version

2

Bits

0ac3b045

Nonce

149,440,032

Timestamp

5/28/2015, 12:02:06 AM

Confirmations

5,724,161

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

bdebd09da758adaf4a102c0d785e0a198bbf09e238e4f6730c60ea41aacf6bea
Transactions (1)
Coinbasebdebd09da758ad…60ea41aacf6bea
1 in β†’ 1 out8.6200 XPM109 B
ANCZAhFA…4XJ8NSvi
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.

7.868 Γ— 10⁹⁸(99-digit number)
78685134919853730793…96229045149172741121
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
7.868 Γ— 10⁹⁸(99-digit number)
78685134919853730793…96229045149172741121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.573 Γ— 10⁹⁹(100-digit number)
15737026983970746158…92458090298345482241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.147 Γ— 10⁹⁹(100-digit number)
31474053967941492317…84916180596690964481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.294 Γ— 10⁹⁹(100-digit number)
62948107935882984634…69832361193381928961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.258 Γ— 10¹⁰⁰(101-digit number)
12589621587176596926…39664722386763857921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.517 Γ— 10¹⁰⁰(101-digit number)
25179243174353193853…79329444773527715841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.035 Γ— 10¹⁰⁰(101-digit number)
50358486348706387707…58658889547055431681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.007 Γ— 10¹⁰¹(102-digit number)
10071697269741277541…17317779094110863361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.014 Γ— 10¹⁰¹(102-digit number)
20143394539482555083…34635558188221726721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.028 Γ— 10¹⁰¹(102-digit number)
40286789078965110166…69271116376443453441
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:57,670,250 XPMΒ·at block #6,803,277 Β· updates every 60s
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