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Block #711,440

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2014, 9:37:30 PM Β· Difficulty 10.9560 Β· 6,106,602 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9f9f7819de635ec5fa4ad9ad1bc012a1144a5142f2a2e43475ba96cf96dec61f
View on Chainz β†—

Height

#711,440

Difficulty

10.955983

Transactions

2

Size

2.45 KB

Version

2

Bits

0af4bb4d

Nonce

291,674,958

Timestamp

9/7/2014, 9:37:30 PM

Confirmations

6,106,602

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4a033454f200e36e1699f7f946167f0e857dbe57843ab96d12a290415be3f51a
Transactions (2)
Coinbaseff6e7c2fa57d55…fab097590b6765
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
8493cf79ea3bd5…b7b56a47f1ce42
15 in β†’ 2 out5310.9609 XPM2.24 KB
ASVgeX9k…eG1Ru5N1AWnAimL4…MAkR7ukp
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.

3.598 Γ— 10⁹⁷(98-digit number)
35989223735174867494…52675432585263237121
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
3.598 Γ— 10⁹⁷(98-digit number)
35989223735174867494…52675432585263237121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.197 Γ— 10⁹⁷(98-digit number)
71978447470349734989…05350865170526474241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.439 Γ— 10⁹⁸(99-digit number)
14395689494069946997…10701730341052948481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.879 Γ— 10⁹⁸(99-digit number)
28791378988139893995…21403460682105896961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.758 Γ— 10⁹⁸(99-digit number)
57582757976279787991…42806921364211793921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.151 Γ— 10⁹⁹(100-digit number)
11516551595255957598…85613842728423587841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.303 Γ— 10⁹⁹(100-digit number)
23033103190511915196…71227685456847175681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.606 Γ— 10⁹⁹(100-digit number)
46066206381023830393…42455370913694351361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.213 Γ— 10⁹⁹(100-digit number)
92132412762047660786…84910741827388702721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.842 Γ— 10¹⁰⁰(101-digit number)
18426482552409532157…69821483654777405441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.685 Γ— 10¹⁰⁰(101-digit number)
36852965104819064314…39642967309554810881
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,788,406 XPMΒ·at block #6,818,041 Β· updates every 60s
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