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Block #2,614,171

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/14/2018, 11:34:16 PM Β· Difficulty 11.2106 Β· 4,230,856 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
26ad5aea7ed68d9c79a7c82730ba951fd04f607e49eca8ff9c840a4e7ba79a1c
View on Chainz β†—

Height

#2,614,171

Difficulty

11.210588

Transactions

1

Size

200 B

Version

2

Bits

0b35e91e

Nonce

1,419,094,782

Timestamp

4/14/2018, 11:34:16 PM

Confirmations

4,230,856

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

8322ae0174efe0ff32045cf7b43afb1e4c782d50235f385cb68ca01a7ca72009
Transactions (1)
Coinbase8322ae0174efe0…8ca01a7ca72009
1 in β†’ 1 out7.9400 XPM110 B
Adqah8zh…1WwoHJ9t
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.

4.037 Γ— 10⁹⁴(95-digit number)
40371419462832266761…94352520351908196571
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
4.037 Γ— 10⁹⁴(95-digit number)
40371419462832266761…94352520351908196571
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.074 Γ— 10⁹⁴(95-digit number)
80742838925664533522…88705040703816393141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.614 Γ— 10⁹⁡(96-digit number)
16148567785132906704…77410081407632786281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.229 Γ— 10⁹⁡(96-digit number)
32297135570265813408…54820162815265572561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.459 Γ— 10⁹⁡(96-digit number)
64594271140531626817…09640325630531145121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.291 Γ— 10⁹⁢(97-digit number)
12918854228106325363…19280651261062290241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.583 Γ— 10⁹⁢(97-digit number)
25837708456212650727…38561302522124580481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.167 Γ— 10⁹⁢(97-digit number)
51675416912425301454…77122605044249160961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.033 Γ— 10⁹⁷(98-digit number)
10335083382485060290…54245210088498321921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.067 Γ— 10⁹⁷(98-digit number)
20670166764970120581…08490420176996643841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.134 Γ— 10⁹⁷(98-digit number)
41340333529940241163…16980840353993287681
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:58,004,641 XPMΒ·at block #6,845,026 Β· updates every 60s
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