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Block #2,812,127

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2018, 11:31:52 AM Β· Difficulty 11.6686 Β· 4,027,371 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b334121d0c05064aead881d9edde07d6c42f4f004326b83ae2c62949ad2e45f9
View on Chainz β†—

Height

#2,812,127

Difficulty

11.668646

Transactions

1

Size

199 B

Version

2

Bits

0bab2c5c

Nonce

730,586,903

Timestamp

8/27/2018, 11:31:52 AM

Confirmations

4,027,371

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

36759a0d396c84fa862175d48507dbf2122d7b872d039f0f845753e406b5222b
Transactions (1)
Coinbase36759a0d396c84…5753e406b5222b
1 in β†’ 1 out7.3300 XPM110 B
AZtxQr2F…7grUWrUz
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.

6.945 Γ— 10⁹²(93-digit number)
69455478426732189502…65434593091845615999
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.945 Γ— 10⁹²(93-digit number)
69455478426732189502…65434593091845615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.389 Γ— 10⁹³(94-digit number)
13891095685346437900…30869186183691231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.778 Γ— 10⁹³(94-digit number)
27782191370692875801…61738372367382463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.556 Γ— 10⁹³(94-digit number)
55564382741385751602…23476744734764927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.111 Γ— 10⁹⁴(95-digit number)
11112876548277150320…46953489469529855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.222 Γ— 10⁹⁴(95-digit number)
22225753096554300640…93906978939059711999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.445 Γ— 10⁹⁴(95-digit number)
44451506193108601281…87813957878119423999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.890 Γ— 10⁹⁴(95-digit number)
88903012386217202563…75627915756238847999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.778 Γ— 10⁹⁡(96-digit number)
17780602477243440512…51255831512477695999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.556 Γ— 10⁹⁡(96-digit number)
35561204954486881025…02511663024955391999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.112 Γ— 10⁹⁡(96-digit number)
71122409908973762050…05023326049910783999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.422 Γ— 10⁹⁢(97-digit number)
14224481981794752410…10046652099821567999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
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