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Block #1,099,684

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/11/2015, 8:32:14 AM Β· Difficulty 10.7603 Β· 5,714,339 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7a9d78656e32813540d4bf17e93bb03cbb7d56996b2be29c1f687c25680d0cf8
View on Chainz β†—

Height

#1,099,684

Difficulty

10.760296

Transactions

1

Size

201 B

Version

2

Bits

0ac2a2ba

Nonce

168,451,831

Timestamp

6/11/2015, 8:32:14 AM

Confirmations

5,714,339

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

3e0e96ebd7a4c060b0da1f3e651050fe7e23ff6bbf7234e0fa3dd54d46601b79
Transactions (1)
Coinbase3e0e96ebd7a4c0…3dd54d46601b79
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.

1.130 Γ— 10⁹⁹(100-digit number)
11303634183269613476…74000034153843328001
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
1.130 Γ— 10⁹⁹(100-digit number)
11303634183269613476…74000034153843328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.260 Γ— 10⁹⁹(100-digit number)
22607268366539226953…48000068307686656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.521 Γ— 10⁹⁹(100-digit number)
45214536733078453907…96000136615373312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.042 Γ— 10⁹⁹(100-digit number)
90429073466156907814…92000273230746624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.808 Γ— 10¹⁰⁰(101-digit number)
18085814693231381562…84000546461493248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.617 Γ— 10¹⁰⁰(101-digit number)
36171629386462763125…68001092922986496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.234 Γ— 10¹⁰⁰(101-digit number)
72343258772925526251…36002185845972992001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.446 Γ— 10¹⁰¹(102-digit number)
14468651754585105250…72004371691945984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.893 Γ— 10¹⁰¹(102-digit number)
28937303509170210500…44008743383891968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.787 Γ— 10¹⁰¹(102-digit number)
57874607018340421001…88017486767783936001
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:57,756,265 XPMΒ·at block #6,814,022 Β· updates every 60s
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