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Block #2,826,264

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/5/2018, 7:59:31 PM Β· Difficulty 11.7103 Β· 4,016,381 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a145fb721c50e7072f7ef7ff34da9f014032261c424eaaa781ed463dc4f9a510
View on Chainz β†—

Height

#2,826,264

Difficulty

11.710263

Transactions

1

Size

201 B

Version

2

Bits

0bb5d3cf

Nonce

1,635,152,772

Timestamp

9/5/2018, 7:59:31 PM

Confirmations

4,016,381

Mined by

⛏️ P2SHALCqhQrBoza2bTZcPH6omdS8Ws7ZwLGshV

Merkle Root

739f86094013553af65545ab7a46b9f5edafb8129e52589d542e355f724d7a82
Transactions (1)
Coinbase739f8609401355…2e355f724d7a82
1 in β†’ 1 out7.2800 XPM110 B
ALCqhQrB…7ZwLGshV
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.

5.781 Γ— 10⁹⁢(97-digit number)
57818178425623133219…78724405600676280321
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
5.781 Γ— 10⁹⁢(97-digit number)
57818178425623133219…78724405600676280321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.156 Γ— 10⁹⁷(98-digit number)
11563635685124626643…57448811201352560641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.312 Γ— 10⁹⁷(98-digit number)
23127271370249253287…14897622402705121281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.625 Γ— 10⁹⁷(98-digit number)
46254542740498506575…29795244805410242561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.250 Γ— 10⁹⁷(98-digit number)
92509085480997013151…59590489610820485121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.850 Γ— 10⁹⁸(99-digit number)
18501817096199402630…19180979221640970241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.700 Γ— 10⁹⁸(99-digit number)
37003634192398805260…38361958443281940481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.400 Γ— 10⁹⁸(99-digit number)
74007268384797610521…76723916886563880961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.480 Γ— 10⁹⁹(100-digit number)
14801453676959522104…53447833773127761921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.960 Γ— 10⁹⁹(100-digit number)
29602907353919044208…06895667546255523841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.920 Γ— 10⁹⁹(100-digit number)
59205814707838088416…13791335092511047681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.184 Γ— 10¹⁰⁰(101-digit number)
11841162941567617683…27582670185022095361
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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