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Block #2,798,648

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2018, 12:09:05 AM Β· Difficulty 11.6787 Β· 4,040,659 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
413d1985c5c41dcd682817ad5cf85524704d6852e7440243ef42c5f243babb8c
View on Chainz β†—

Height

#2,798,648

Difficulty

11.678700

Transactions

1

Size

200 B

Version

2

Bits

0badbf42

Nonce

443,192,604

Timestamp

8/18/2018, 12:09:05 AM

Confirmations

4,040,659

Mined by

⛏️ P2SHALG1HFLP163Xyw3cVv5YeRR9niymMBqFUC

Merkle Root

60b2233772ce6b0d0c629cba860b4a8b633d8b0b954267000952ed380f3ab230
Transactions (1)
Coinbase60b2233772ce6b…52ed380f3ab230
1 in β†’ 1 out7.3200 XPM110 B
ALG1HFLP…ymMBqFUC
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.

3.095 Γ— 10⁹⁴(95-digit number)
30951108164615451182…66781967381822262081
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
3.095 Γ— 10⁹⁴(95-digit number)
30951108164615451182…66781967381822262081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.190 Γ— 10⁹⁴(95-digit number)
61902216329230902365…33563934763644524161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.238 Γ— 10⁹⁡(96-digit number)
12380443265846180473…67127869527289048321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.476 Γ— 10⁹⁡(96-digit number)
24760886531692360946…34255739054578096641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.952 Γ— 10⁹⁡(96-digit number)
49521773063384721892…68511478109156193281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.904 Γ— 10⁹⁡(96-digit number)
99043546126769443784…37022956218312386561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.980 Γ— 10⁹⁢(97-digit number)
19808709225353888756…74045912436624773121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.961 Γ— 10⁹⁢(97-digit number)
39617418450707777513…48091824873249546241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.923 Γ— 10⁹⁢(97-digit number)
79234836901415555027…96183649746499092481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.584 Γ— 10⁹⁷(98-digit number)
15846967380283111005…92367299492998184961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.169 Γ— 10⁹⁷(98-digit number)
31693934760566222010…84734598985996369921
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:57,958,738 XPMΒ·at block #6,839,306 Β· updates every 60s
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