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Block #2,133,331

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/26/2017, 10:42:37 AM Β· Difficulty 10.9097 Β· 4,706,935 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3ce99075c06c962dd9353c262b6006d52778dddfc4dbea57d6576c990dafc0d2
View on Chainz β†—

Height

#2,133,331

Difficulty

10.909697

Transactions

1

Size

198 B

Version

2

Bits

0ae8e1ec

Nonce

1,040,558,878

Timestamp

5/26/2017, 10:42:37 AM

Confirmations

4,706,935

Mined by

⛏️ P2SHATco4z1qC5YFd68w7MdRYhzfiUSPNZjmUe

Merkle Root

72b310079e026354af66524c79fe7bae62249683a7c361ebe1efb7e821987e55
Transactions (1)
Coinbase72b310079e0263…efb7e821987e55
1 in β†’ 1 out8.3900 XPM109 B
ATco4z1q…SPNZjmUe
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.

9.483 Γ— 10⁹²(93-digit number)
94833110570034026720…23790633430762875039
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
9.483 Γ— 10⁹²(93-digit number)
94833110570034026720…23790633430762875039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.896 Γ— 10⁹³(94-digit number)
18966622114006805344…47581266861525750079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.793 Γ— 10⁹³(94-digit number)
37933244228013610688…95162533723051500159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.586 Γ— 10⁹³(94-digit number)
75866488456027221376…90325067446103000319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.517 Γ— 10⁹⁴(95-digit number)
15173297691205444275…80650134892206000639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.034 Γ— 10⁹⁴(95-digit number)
30346595382410888550…61300269784412001279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.069 Γ— 10⁹⁴(95-digit number)
60693190764821777100…22600539568824002559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.213 Γ— 10⁹⁡(96-digit number)
12138638152964355420…45201079137648005119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.427 Γ— 10⁹⁡(96-digit number)
24277276305928710840…90402158275296010239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.855 Γ— 10⁹⁡(96-digit number)
48554552611857421680…80804316550592020479
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:57,966,442 XPMΒ·at block #6,840,265 Β· updates every 60s
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