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Block #2,680,216

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/27/2018, 1:48:10 PM Β· Difficulty 11.6918 Β· 4,161,451 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7065abab9881cc8c4a441994f314e2c68c283ff28e5f99def00dfd9d64a1a6a0
View on Chainz β†—

Height

#2,680,216

Difficulty

11.691794

Transactions

2

Size

427 B

Version

2

Bits

0bb1196d

Nonce

6,943,557

Timestamp

5/27/2018, 1:48:10 PM

Confirmations

4,161,451

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

1c63bc3005876a33f757e105b4ff1782a31e3701f2f3a484dedba2127fc6bb95
Transactions (2)
Coinbase91bafc0d10bbca…e34c7d515c2757
1 in β†’ 1 out7.3100 XPM110 B
Adqah8zh…1WwoHJ9t
a571f58cd93868…94eb1a866726d2
1 in β†’ 2 out2.2773 XPM227 B
AVU8JbJb…f9v26UuVAMFxoiZV…2UX5WRMn
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.

5.250 Γ— 10⁹⁡(96-digit number)
52505628719181575557…98934277624245888001
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
5.250 Γ— 10⁹⁡(96-digit number)
52505628719181575557…98934277624245888001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.050 Γ— 10⁹⁢(97-digit number)
10501125743836315111…97868555248491776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.100 Γ— 10⁹⁢(97-digit number)
21002251487672630223…95737110496983552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.200 Γ— 10⁹⁢(97-digit number)
42004502975345260446…91474220993967104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.400 Γ— 10⁹⁢(97-digit number)
84009005950690520892…82948441987934208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.680 Γ— 10⁹⁷(98-digit number)
16801801190138104178…65896883975868416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.360 Γ— 10⁹⁷(98-digit number)
33603602380276208356…31793767951736832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.720 Γ— 10⁹⁷(98-digit number)
67207204760552416713…63587535903473664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.344 Γ— 10⁹⁸(99-digit number)
13441440952110483342…27175071806947328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.688 Γ— 10⁹⁸(99-digit number)
26882881904220966685…54350143613894656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.376 Γ— 10⁹⁸(99-digit number)
53765763808441933371…08700287227789312001
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:57,977,725 XPMΒ·at block #6,841,666 Β· updates every 60s
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