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Block #857,450

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/17/2014, 8:31:37 PM Β· Difficulty 10.9675 Β· 5,984,336 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1c11cc4df434ae5594fa43e17cf933915e451bf5d3a9e2fe68cbad9172655cc9
View on Chainz β†—

Height

#857,450

Difficulty

10.967516

Transactions

2

Size

433 B

Version

2

Bits

0af7af19

Nonce

1,125,827,943

Timestamp

12/17/2014, 8:31:37 PM

Confirmations

5,984,336

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4b6d4ea93d97285a4f1d8137b7b23237085b23691995ebda9cfa4b8e37ddb473
Transactions (2)
Coinbase508c4a6d933895…88bc1d0d984887
1 in β†’ 1 out8.3150 XPM116 B
ANSXnLY2…Sd25TjkD
ca80bdcc5bf7a8…2c93967ed32fec
1 in β†’ 2 out0.0381 XPM226 B
ATKmMxZt…wRFReoVnAddXjEX1…x2y2a4xz
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.

2.629 Γ— 10⁹⁢(97-digit number)
26296491582475865881…43006436561393630721
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
2.629 Γ— 10⁹⁢(97-digit number)
26296491582475865881…43006436561393630721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.259 Γ— 10⁹⁢(97-digit number)
52592983164951731762…86012873122787261441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.051 Γ— 10⁹⁷(98-digit number)
10518596632990346352…72025746245574522881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.103 Γ— 10⁹⁷(98-digit number)
21037193265980692705…44051492491149045761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.207 Γ— 10⁹⁷(98-digit number)
42074386531961385410…88102984982298091521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.414 Γ— 10⁹⁷(98-digit number)
84148773063922770820…76205969964596183041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.682 Γ— 10⁹⁸(99-digit number)
16829754612784554164…52411939929192366081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.365 Γ— 10⁹⁸(99-digit number)
33659509225569108328…04823879858384732161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.731 Γ— 10⁹⁸(99-digit number)
67319018451138216656…09647759716769464321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.346 Γ— 10⁹⁹(100-digit number)
13463803690227643331…19295519433538928641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.692 Γ— 10⁹⁹(100-digit number)
26927607380455286662…38591038867077857281
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:57,978,666 XPMΒ·at block #6,841,785 Β· updates every 60s
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