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Block #2,679,840

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/27/2018, 7:13:07 AM Β· Difficulty 11.6929 Β· 4,153,653 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9968cfec6e6ea495a86c29fabf9844884a3b426117f55e24d97b52c7bbbe5190
View on Chainz β†—

Height

#2,679,840

Difficulty

11.692908

Transactions

2

Size

867 B

Version

2

Bits

0bb16272

Nonce

336,173,001

Timestamp

5/27/2018, 7:13:07 AM

Confirmations

4,153,653

Mined by

⛏️ P2SHAJ8Po7zGyni9FSHYHSV3HzFLs9gont85Mz

Merkle Root

19ae07904ddfa2772e7db1a47fb05684925f0c7b327a2c285b211f6391b6e86e
Transactions (2)
Coinbase9ba9cb0e4fc568…c5ee3e7406b463
1 in β†’ 1 out7.3100 XPM110 B
AJ8Po7zG…gont85Mz
80da499d05aacb…87096a6ecae4ae
4 in β†’ 2 out245.4269 XPM668 B
AQmjqzoU…5U6sbve9Adgo6V4T…H2msc5Le
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.

1.608 Γ— 10⁹³(94-digit number)
16087616409826365258…62388435826131814401
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
1.608 Γ— 10⁹³(94-digit number)
16087616409826365258…62388435826131814401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.217 Γ— 10⁹³(94-digit number)
32175232819652730517…24776871652263628801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.435 Γ— 10⁹³(94-digit number)
64350465639305461034…49553743304527257601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.287 Γ— 10⁹⁴(95-digit number)
12870093127861092206…99107486609054515201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.574 Γ— 10⁹⁴(95-digit number)
25740186255722184413…98214973218109030401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.148 Γ— 10⁹⁴(95-digit number)
51480372511444368827…96429946436218060801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.029 Γ— 10⁹⁡(96-digit number)
10296074502288873765…92859892872436121601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.059 Γ— 10⁹⁡(96-digit number)
20592149004577747530…85719785744872243201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.118 Γ— 10⁹⁡(96-digit number)
41184298009155495061…71439571489744486401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.236 Γ— 10⁹⁡(96-digit number)
82368596018310990123…42879142979488972801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.647 Γ— 10⁹⁢(97-digit number)
16473719203662198024…85758285958977945601
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:57,912,148 XPMΒ·at block #6,833,492 Β· updates every 60s
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