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Block #2,654,280

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2018, 4:20:21 AM Β· Difficulty 11.7230 Β· 4,189,743 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8824fc87d73226ea8beb2994afd4559f21fbba9d8405615efd333d0d9a653ddb
View on Chainz β†—

Height

#2,654,280

Difficulty

11.723050

Transactions

2

Size

1019 B

Version

2

Bits

0bb919cc

Nonce

240,531,195

Timestamp

5/9/2018, 4:20:21 AM

Confirmations

4,189,743

Mined by

⛏️ P2SHAShSAZ7FjuCBRFuq2nmmM5BxtNCnx2cEfe

Merkle Root

4dc3d1ab85f194eb036de7321fae362c8d7bbf9884704897c54b9b0d202d28c2
Transactions (2)
Coinbaseb28f13143fab48…32b12438161048
1 in β†’ 1 out7.2700 XPM110 B
AShSAZ7F…Cnx2cEfe
4b2835a87aa870…d1fbff0f990e94
5 in β†’ 2 out9921.8300 XPM819 B
AH181h1x…oEJEzVkEAUz98Ghc…BK6rbrpN
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.

5.147 Γ— 10⁹⁴(95-digit number)
51470337931924729062…36954972809868970731
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
5.147 Γ— 10⁹⁴(95-digit number)
51470337931924729062…36954972809868970731
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.029 Γ— 10⁹⁡(96-digit number)
10294067586384945812…73909945619737941461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.058 Γ— 10⁹⁡(96-digit number)
20588135172769891624…47819891239475882921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.117 Γ— 10⁹⁡(96-digit number)
41176270345539783249…95639782478951765841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.235 Γ— 10⁹⁡(96-digit number)
82352540691079566499…91279564957903531681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.647 Γ— 10⁹⁢(97-digit number)
16470508138215913299…82559129915807063361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.294 Γ— 10⁹⁢(97-digit number)
32941016276431826599…65118259831614126721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.588 Γ— 10⁹⁢(97-digit number)
65882032552863653199…30236519663228253441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.317 Γ— 10⁹⁷(98-digit number)
13176406510572730639…60473039326456506881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.635 Γ— 10⁹⁷(98-digit number)
26352813021145461279…20946078652913013761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.270 Γ— 10⁹⁷(98-digit number)
52705626042290922559…41892157305826027521
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:57,996,566 XPMΒ·at block #6,844,022 Β· updates every 60s
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