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Block #2,801,905

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2018, 8:36:07 AM Β· Difficulty 11.6704 Β· 4,040,939 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bad87d9a0872bb4e06a42c4ce726eee099786322e409c521677d4aaf947962cf
View on Chainz β†—

Height

#2,801,905

Difficulty

11.670390

Transactions

1

Size

200 B

Version

2

Bits

0bab9ea7

Nonce

21,812,202

Timestamp

8/20/2018, 8:36:07 AM

Confirmations

4,040,939

Mined by

⛏️ P2SHAYWCydiHgMdrdWkJSj4cRFy2QDW7hgPFkC

Merkle Root

cd3ff5cc3a69aa64daf220408627a58cc079b5546f7638b8e7122816de9a2225
Transactions (1)
Coinbasecd3ff5cc3a69aa…122816de9a2225
1 in β†’ 1 out7.3300 XPM110 B
AYWCydiH…W7hgPFkC
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.

2.766 Γ— 10⁹⁡(96-digit number)
27661990485921849316…25593394527854647041
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
2.766 Γ— 10⁹⁡(96-digit number)
27661990485921849316…25593394527854647041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.532 Γ— 10⁹⁡(96-digit number)
55323980971843698633…51186789055709294081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.106 Γ— 10⁹⁢(97-digit number)
11064796194368739726…02373578111418588161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.212 Γ— 10⁹⁢(97-digit number)
22129592388737479453…04747156222837176321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.425 Γ— 10⁹⁢(97-digit number)
44259184777474958906…09494312445674352641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.851 Γ— 10⁹⁢(97-digit number)
88518369554949917813…18988624891348705281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.770 Γ— 10⁹⁷(98-digit number)
17703673910989983562…37977249782697410561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.540 Γ— 10⁹⁷(98-digit number)
35407347821979967125…75954499565394821121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.081 Γ— 10⁹⁷(98-digit number)
70814695643959934250…51908999130789642241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.416 Γ— 10⁹⁸(99-digit number)
14162939128791986850…03817998261579284481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.832 Γ— 10⁹⁸(99-digit number)
28325878257583973700…07635996523158568961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
5.665 Γ— 10⁹⁸(99-digit number)
56651756515167947400…15271993046317137921
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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