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Block #2,799,438

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/18/2018, 2:03:55 PM Β· Difficulty 11.6758 Β· 4,042,807 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
67c1e5f92e99965bd36d29a33080946a2d95cbd6e857ad0a8fe32add2dea5ca0
View on Chainz β†—

Height

#2,799,438

Difficulty

11.675832

Transactions

1

Size

200 B

Version

2

Bits

0bad034f

Nonce

1,307,846,961

Timestamp

8/18/2018, 2:03:55 PM

Confirmations

4,042,807

Mined by

⛏️ P2SHATnaoRatCp3DGtUY4MU3jS1Skp1eavWSZp

Merkle Root

b8d2fa1fd5b5892d528e48ba6a64264af4e70eea9c0c7580a5a6ad6c4a5c8902
Transactions (1)
Coinbaseb8d2fa1fd5b589…a6ad6c4a5c8902
1 in β†’ 1 out7.3200 XPM109 B
ATnaoRat…1eavWSZp
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.

2.337 Γ— 10⁹⁢(97-digit number)
23372637626645621024…94819907215998023679
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
2.337 Γ— 10⁹⁢(97-digit number)
23372637626645621024…94819907215998023679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.674 Γ— 10⁹⁢(97-digit number)
46745275253291242048…89639814431996047359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.349 Γ— 10⁹⁢(97-digit number)
93490550506582484096…79279628863992094719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.869 Γ— 10⁹⁷(98-digit number)
18698110101316496819…58559257727984189439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.739 Γ— 10⁹⁷(98-digit number)
37396220202632993638…17118515455968378879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.479 Γ— 10⁹⁷(98-digit number)
74792440405265987277…34237030911936757759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.495 Γ— 10⁹⁸(99-digit number)
14958488081053197455…68474061823873515519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.991 Γ— 10⁹⁸(99-digit number)
29916976162106394910…36948123647747031039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.983 Γ— 10⁹⁸(99-digit number)
59833952324212789821…73896247295494062079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.196 Γ— 10⁹⁹(100-digit number)
11966790464842557964…47792494590988124159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.393 Γ— 10⁹⁹(100-digit number)
23933580929685115928…95584989181976248319
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,982,358 XPMΒ·at block #6,842,244 Β· updates every 60s
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