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Block #2,924,824

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/16/2018, 2:25:25 AM Β· Difficulty 11.3573 Β· 3,917,139 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b556dc64d930217d86467af87d2860e4336959c6aec1652d2a83e1f37b6f4e4b
View on Chainz β†—

Height

#2,924,824

Difficulty

11.357281

Transactions

1

Size

200 B

Version

2

Bits

0b5b76c0

Nonce

139,507,320

Timestamp

11/16/2018, 2:25:25 AM

Confirmations

3,917,139

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

3153355ff5a3bb6b49787e546ac26aae5ec4433976613acfdb6a1cdb67d0cd86
Transactions (1)
Coinbase3153355ff5a3bb…6a1cdb67d0cd86
1 in β†’ 1 out7.7400 XPM110 B
AUhjokok…k5m93PZR
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.

6.607 Γ— 10⁹⁡(96-digit number)
66073634209229928109…42569785223346165761
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
6.607 Γ— 10⁹⁡(96-digit number)
66073634209229928109…42569785223346165761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.321 Γ— 10⁹⁢(97-digit number)
13214726841845985621…85139570446692331521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.642 Γ— 10⁹⁢(97-digit number)
26429453683691971243…70279140893384663041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.285 Γ— 10⁹⁢(97-digit number)
52858907367383942487…40558281786769326081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.057 Γ— 10⁹⁷(98-digit number)
10571781473476788497…81116563573538652161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.114 Γ— 10⁹⁷(98-digit number)
21143562946953576994…62233127147077304321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.228 Γ— 10⁹⁷(98-digit number)
42287125893907153989…24466254294154608641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.457 Γ— 10⁹⁷(98-digit number)
84574251787814307979…48932508588309217281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.691 Γ— 10⁹⁸(99-digit number)
16914850357562861595…97865017176618434561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.382 Γ— 10⁹⁸(99-digit number)
33829700715125723191…95730034353236869121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.765 Γ— 10⁹⁸(99-digit number)
67659401430251446383…91460068706473738241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.353 Γ— 10⁹⁹(100-digit number)
13531880286050289276…82920137412947476481
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
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