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Block #2,762,911

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/24/2018, 10:06:50 AM Β· Difficulty 11.6553 Β· 4,077,274 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cce758eb6dc2a77a478d4f446f877373c488315e21154341981b24e34cc20c2c
View on Chainz β†—

Height

#2,762,911

Difficulty

11.655344

Transactions

1

Size

201 B

Version

2

Bits

0ba7c499

Nonce

824,715,607

Timestamp

7/24/2018, 10:06:50 AM

Confirmations

4,077,274

Mined by

⛏️ P2SHANXKsEDpZa7FQk4na1YXeRj7pCmzdusdgP

Merkle Root

526ba2494d7354a02cb3c7fba3d09e25ee32f0bf23e6d97263acc868b34a2e43
Transactions (1)
Coinbase526ba2494d7354…acc868b34a2e43
1 in β†’ 1 out7.3500 XPM110 B
ANXKsEDp…mzdusdgP
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.

1.422 Γ— 10⁹⁷(98-digit number)
14224494857783556627…06386313407085578241
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
1.422 Γ— 10⁹⁷(98-digit number)
14224494857783556627…06386313407085578241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.844 Γ— 10⁹⁷(98-digit number)
28448989715567113255…12772626814171156481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.689 Γ— 10⁹⁷(98-digit number)
56897979431134226510…25545253628342312961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.137 Γ— 10⁹⁸(99-digit number)
11379595886226845302…51090507256684625921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.275 Γ— 10⁹⁸(99-digit number)
22759191772453690604…02181014513369251841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.551 Γ— 10⁹⁸(99-digit number)
45518383544907381208…04362029026738503681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.103 Γ— 10⁹⁸(99-digit number)
91036767089814762416…08724058053477007361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.820 Γ— 10⁹⁹(100-digit number)
18207353417962952483…17448116106954014721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.641 Γ— 10⁹⁹(100-digit number)
36414706835925904966…34896232213908029441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.282 Γ— 10⁹⁹(100-digit number)
72829413671851809933…69792464427816058881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.456 Γ— 10¹⁰⁰(101-digit number)
14565882734370361986…39584928855632117761
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,965,803 XPMΒ·at block #6,840,184 Β· updates every 60s
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