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Block #2,641,842

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 12:21:12 PM Β· Difficulty 11.6337 Β· 4,191,638 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2dca01da6856f3a1562d204f74a61d2ab9744fb1ddec00804df9e4d7afdd8149
View on Chainz β†—

Height

#2,641,842

Difficulty

11.633734

Transactions

2

Size

61.86 KB

Version

2

Bits

0ba23c67

Nonce

918,292,659

Timestamp

5/1/2018, 12:21:12 PM

Confirmations

4,191,638

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

acf3029d4ec04e18b2f76a1a61efb9bd77b570e15eca991631b09953125b3e67
Transactions (2)
Coinbaseaaa83fb168402f…6684ae8015a1ea
1 in β†’ 1 out8.1500 XPM110 B
Adqah8zh…1WwoHJ9t
ae6e63e7475897…83a32c938b84cb
426 in β†’ 2 out5000.0100 XPM61.67 KB
ALPF8J52…Hjw4BMsGAP14A44c…5CepkGPb
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.

5.722 Γ— 10⁹³(94-digit number)
57223088414499023919…39158027425523147641
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
5.722 Γ— 10⁹³(94-digit number)
57223088414499023919…39158027425523147641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.144 Γ— 10⁹⁴(95-digit number)
11444617682899804783…78316054851046295281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.288 Γ— 10⁹⁴(95-digit number)
22889235365799609567…56632109702092590561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.577 Γ— 10⁹⁴(95-digit number)
45778470731599219135…13264219404185181121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.155 Γ— 10⁹⁴(95-digit number)
91556941463198438271…26528438808370362241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.831 Γ— 10⁹⁡(96-digit number)
18311388292639687654…53056877616740724481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.662 Γ— 10⁹⁡(96-digit number)
36622776585279375308…06113755233481448961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.324 Γ— 10⁹⁡(96-digit number)
73245553170558750617…12227510466962897921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.464 Γ— 10⁹⁢(97-digit number)
14649110634111750123…24455020933925795841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.929 Γ— 10⁹⁢(97-digit number)
29298221268223500246…48910041867851591681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.859 Γ— 10⁹⁢(97-digit number)
58596442536447000493…97820083735703183361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.171 Γ— 10⁹⁷(98-digit number)
11719288507289400098…95640167471406366721
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,912,044 XPMΒ·at block #6,833,479 Β· updates every 60s
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