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Block #2,189,342

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/2/2017, 10:37:16 AM Β· Difficulty 10.9486 Β· 4,624,695 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a6dfea7174046b59f8d6c895cf6052af39e064a40d407cefaacd015ddbc0dc7c
View on Chainz β†—

Height

#2,189,342

Difficulty

10.948555

Transactions

2

Size

426 B

Version

2

Bits

0af2d47c

Nonce

1,231,219,819

Timestamp

7/2/2017, 10:37:16 AM

Confirmations

4,624,695

Mined by

⛏️ P2SHAJeorTKPgH3VwuwewUKceYoHAHMT8FnA6K

Merkle Root

2284701534d59202039c633129c4acd2dc502b656941074211a06df41b3dc5bd
Transactions (2)
Coinbase895cbcf2bb98df…29dce9b0571de4
1 in β†’ 1 out8.3400 XPM110 B
AJeorTKP…MT8FnA6K
7f3209af56a5d4…ec44ad914f56cd
1 in β†’ 2 out1.0087 XPM226 B
AQg71Mwj…h1XZjKG3ATiCn4EF…UetKStY7
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.

1.022 Γ— 10⁹⁴(95-digit number)
10225011500783743853…05795408566753290721
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
1.022 Γ— 10⁹⁴(95-digit number)
10225011500783743853…05795408566753290721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.045 Γ— 10⁹⁴(95-digit number)
20450023001567487706…11590817133506581441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.090 Γ— 10⁹⁴(95-digit number)
40900046003134975413…23181634267013162881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.180 Γ— 10⁹⁴(95-digit number)
81800092006269950826…46363268534026325761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.636 Γ— 10⁹⁡(96-digit number)
16360018401253990165…92726537068052651521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.272 Γ— 10⁹⁡(96-digit number)
32720036802507980330…85453074136105303041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.544 Γ— 10⁹⁡(96-digit number)
65440073605015960661…70906148272210606081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.308 Γ— 10⁹⁢(97-digit number)
13088014721003192132…41812296544421212161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.617 Γ— 10⁹⁢(97-digit number)
26176029442006384264…83624593088842424321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.235 Γ— 10⁹⁢(97-digit number)
52352058884012768529…67249186177684848641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.047 Γ— 10⁹⁷(98-digit number)
10470411776802553705…34498372355369697281
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:57,756,371 XPMΒ·at block #6,814,036 Β· updates every 60s
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