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Block #2,814,254

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/28/2018, 7:45:57 PM Β· Difficulty 11.6811 Β· 4,027,740 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a4fe5673f87a3dcfcbf1aae34e5c1fcc29e9f700216285522df6d6bb4d29d9f2
View on Chainz β†—

Height

#2,814,254

Difficulty

11.681073

Transactions

1

Size

201 B

Version

2

Bits

0bae5acd

Nonce

1,399,282,971

Timestamp

8/28/2018, 7:45:57 PM

Confirmations

4,027,740

Mined by

⛏️ P2SHAMV9RSR43hUkQpEJaHQHaw8kJqTu6yFmiG

Merkle Root

ba09393480c9e09758e1ef8195de3f91c891c49c99f2c2e02806cbc7d386c87d
Transactions (1)
Coinbaseba09393480c9e0…06cbc7d386c87d
1 in β†’ 1 out7.3200 XPM110 B
AMV9RSR4…Tu6yFmiG
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.

2.030 Γ— 10⁹⁷(98-digit number)
20304363644486726479…93894016122213921279
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
2.030 Γ— 10⁹⁷(98-digit number)
20304363644486726479…93894016122213921279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.060 Γ— 10⁹⁷(98-digit number)
40608727288973452958…87788032244427842559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.121 Γ— 10⁹⁷(98-digit number)
81217454577946905917…75576064488855685119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.624 Γ— 10⁹⁸(99-digit number)
16243490915589381183…51152128977711370239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.248 Γ— 10⁹⁸(99-digit number)
32486981831178762366…02304257955422740479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.497 Γ— 10⁹⁸(99-digit number)
64973963662357524733…04608515910845480959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.299 Γ— 10⁹⁹(100-digit number)
12994792732471504946…09217031821690961919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.598 Γ— 10⁹⁹(100-digit number)
25989585464943009893…18434063643381923839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.197 Γ— 10⁹⁹(100-digit number)
51979170929886019786…36868127286763847679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.039 Γ— 10¹⁰⁰(101-digit number)
10395834185977203957…73736254573527695359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.079 Γ— 10¹⁰⁰(101-digit number)
20791668371954407914…47472509147055390719
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,980,340 XPMΒ·at block #6,841,993 Β· updates every 60s
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