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Block #1,286,296

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/17/2015, 3:06:51 PM Β· Difficulty 10.8441 Β· 5,530,463 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f25a8f63c10fca6c0d9e6db89f6b2bc81069928d6e84a44543c3af6534126ef1
View on Chainz β†—

Height

#1,286,296

Difficulty

10.844076

Transactions

2

Size

1.43 KB

Version

2

Bits

0ad81562

Nonce

250,235,391

Timestamp

10/17/2015, 3:06:51 PM

Confirmations

5,530,463

Mined by

⛏️ P2SHAPfNGzLEZivEezFzfAxENhHBch8jtAWTpz

Merkle Root

a60971260d6095d663714a59c19c03ca437443ed7b92c303956be66ff76e632d
Transactions (2)
Coinbase74a8bca3e953e1…14d8055b371859
1 in β†’ 1 out9.2500 XPM110 B
APfNGzLE…8jtAWTpz
ba0a044d47cf84…ea0db35ef4f501
8 in β†’ 2 out4000.0100 XPM1.23 KB
AGSmzk18…hH9qRFZqAWpXhem9…NExsJXnt
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.

7.168 Γ— 10⁹⁴(95-digit number)
71684979113870822488…09309991095738256001
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
7.168 Γ— 10⁹⁴(95-digit number)
71684979113870822488…09309991095738256001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.433 Γ— 10⁹⁡(96-digit number)
14336995822774164497…18619982191476512001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.867 Γ— 10⁹⁡(96-digit number)
28673991645548328995…37239964382953024001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.734 Γ— 10⁹⁡(96-digit number)
57347983291096657990…74479928765906048001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.146 Γ— 10⁹⁢(97-digit number)
11469596658219331598…48959857531812096001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.293 Γ— 10⁹⁢(97-digit number)
22939193316438663196…97919715063624192001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.587 Γ— 10⁹⁢(97-digit number)
45878386632877326392…95839430127248384001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.175 Γ— 10⁹⁢(97-digit number)
91756773265754652785…91678860254496768001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.835 Γ— 10⁹⁷(98-digit number)
18351354653150930557…83357720508993536001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.670 Γ— 10⁹⁷(98-digit number)
36702709306301861114…66715441017987072001
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:57,778,103 XPMΒ·at block #6,816,758 Β· updates every 60s
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