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Block #2,099,733

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2017, 4:54:29 PM Β· Difficulty 10.8562 Β· 4,741,291 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0d14a86e3eaf5cb6a2f4fc5e901d2df0f707c7af09bcad1d1e576d4319c61ad0
View on Chainz β†—

Height

#2,099,733

Difficulty

10.856239

Transactions

1

Size

199 B

Version

2

Bits

0adb3276

Nonce

1,526,790,049

Timestamp

5/4/2017, 4:54:29 PM

Confirmations

4,741,291

Mined by

⛏️ P2SHATMYaDcWvk4jwhdHkF166Z2vRe6KN7i4F4

Merkle Root

12cd834af9914f546b6c42adca330c8c5b0cb30216845341c9e7ac06e4ca07db
Transactions (1)
Coinbase12cd834af9914f…e7ac06e4ca07db
1 in β†’ 1 out8.4700 XPM109 B
ATMYaDcW…6KN7i4F4
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.

2.118 Γ— 10⁹⁡(96-digit number)
21182541872853653919…18024091866336735999
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.118 Γ— 10⁹⁡(96-digit number)
21182541872853653919…18024091866336735999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.236 Γ— 10⁹⁡(96-digit number)
42365083745707307839…36048183732673471999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.473 Γ— 10⁹⁡(96-digit number)
84730167491414615678…72096367465346943999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.694 Γ— 10⁹⁢(97-digit number)
16946033498282923135…44192734930693887999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.389 Γ— 10⁹⁢(97-digit number)
33892066996565846271…88385469861387775999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.778 Γ— 10⁹⁢(97-digit number)
67784133993131692543…76770939722775551999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.355 Γ— 10⁹⁷(98-digit number)
13556826798626338508…53541879445551103999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.711 Γ— 10⁹⁷(98-digit number)
27113653597252677017…07083758891102207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.422 Γ— 10⁹⁷(98-digit number)
54227307194505354034…14167517782204415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.084 Γ— 10⁹⁸(99-digit number)
10845461438901070806…28335035564408831999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,972,549 XPMΒ·at block #6,841,023 Β· updates every 60s
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