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Block #2,691,641

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2018, 2:53:33 PM Β· Difficulty 11.6822 Β· 4,141,733 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b0e255218301f0fd2e5a77ffd2d8e0b18ed7c6965949f42ad8b0d9ae7c6eb2a5
View on Chainz β†—

Height

#2,691,641

Difficulty

11.682183

Transactions

2

Size

2.44 KB

Version

2

Bits

0baea38d

Nonce

203,794,307

Timestamp

6/4/2018, 2:53:33 PM

Confirmations

4,141,733

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

dbc4224a2b9e2f5b2836aae835f912dd4213acc63df633d36084f9094309fa5b
Transactions (2)
Coinbasec9f8577d58555d…0d122933486b58
1 in β†’ 1 out7.3500 XPM109 B
Adqah8zh…1WwoHJ9t
e83ae961206bc8…247e71bba26438
15 in β†’ 2 out122.0600 XPM2.24 KB
ARY67Yio…VS88Q8ouAVmew3vn…KGB14vti
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.

1.280 Γ— 10⁹⁡(96-digit number)
12803705190351083165…36884451397958221441
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
1.280 Γ— 10⁹⁡(96-digit number)
12803705190351083165…36884451397958221441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.560 Γ— 10⁹⁡(96-digit number)
25607410380702166331…73768902795916442881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.121 Γ— 10⁹⁡(96-digit number)
51214820761404332663…47537805591832885761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.024 Γ— 10⁹⁢(97-digit number)
10242964152280866532…95075611183665771521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.048 Γ— 10⁹⁢(97-digit number)
20485928304561733065…90151222367331543041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.097 Γ— 10⁹⁢(97-digit number)
40971856609123466130…80302444734663086081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.194 Γ— 10⁹⁢(97-digit number)
81943713218246932261…60604889469326172161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.638 Γ— 10⁹⁷(98-digit number)
16388742643649386452…21209778938652344321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.277 Γ— 10⁹⁷(98-digit number)
32777485287298772904…42419557877304688641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.555 Γ— 10⁹⁷(98-digit number)
65554970574597545809…84839115754609377281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.311 Γ— 10⁹⁸(99-digit number)
13110994114919509161…69678231509218754561
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:57,911,188 XPMΒ·at block #6,833,373 Β· updates every 60s
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