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Block #2,825,839

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/5/2018, 12:57:27 PM Β· Difficulty 11.7101 Β· 4,011,017 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6f635d60b02cea00ba360b642c1a206f63d8e3e49157f6a81c094f17f46fcb58
View on Chainz β†—

Height

#2,825,839

Difficulty

11.710067

Transactions

1

Size

200 B

Version

2

Bits

0bb5c6f0

Nonce

873,152,092

Timestamp

9/5/2018, 12:57:27 PM

Confirmations

4,011,017

Mined by

⛏️ P2SHAPbrtMF7VFA2X7MnApiVJ25Gqa6VGCinZV

Merkle Root

4aa4cbd06b28e0d17d0f355612056bd88835a8e9c19acda53d79935b14f6368f
Transactions (1)
Coinbase4aa4cbd06b28e0…79935b14f6368f
1 in β†’ 1 out7.2800 XPM110 B
APbrtMF7…6VGCinZV
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.

8.168 Γ— 10⁹⁴(95-digit number)
81684864432425451043…82195222239300703331
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
8.168 Γ— 10⁹⁴(95-digit number)
81684864432425451043…82195222239300703331
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.633 Γ— 10⁹⁡(96-digit number)
16336972886485090208…64390444478601406661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.267 Γ— 10⁹⁡(96-digit number)
32673945772970180417…28780888957202813321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.534 Γ— 10⁹⁡(96-digit number)
65347891545940360835…57561777914405626641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.306 Γ— 10⁹⁢(97-digit number)
13069578309188072167…15123555828811253281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.613 Γ— 10⁹⁢(97-digit number)
26139156618376144334…30247111657622506561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.227 Γ— 10⁹⁢(97-digit number)
52278313236752288668…60494223315245013121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.045 Γ— 10⁹⁷(98-digit number)
10455662647350457733…20988446630490026241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.091 Γ— 10⁹⁷(98-digit number)
20911325294700915467…41976893260980052481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.182 Γ— 10⁹⁷(98-digit number)
41822650589401830934…83953786521960104961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.364 Γ— 10⁹⁷(98-digit number)
83645301178803661868…67907573043920209921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.672 Γ— 10⁹⁸(99-digit number)
16729060235760732373…35815146087840419841
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,939,136 XPMΒ·at block #6,836,855 Β· updates every 60s
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