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Block #2,864,129

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/2/2018, 1:56:09 PM Β· Difficulty 11.6717 Β· 3,978,051 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
74564bd63483b7d3775e65d6ef7aebb7cd2fd0e1c9b4b5972dbedbec8bfd9f6b
View on Chainz β†—

Height

#2,864,129

Difficulty

11.671708

Transactions

2

Size

1.14 KB

Version

2

Bits

0babf50c

Nonce

873,841,575

Timestamp

10/2/2018, 1:56:09 PM

Confirmations

3,978,051

Mined by

⛏️ P2SHAHenD23Raqgz2aUVbkvjw1z2Pn6e3e6M6c

Merkle Root

54214d261b23a6e033481bfca481512656513b2a58cab7bd82524c15ef1882dc
Transactions (2)
Coinbase52b729bcdaee52…fd39169c8c487e
1 in β†’ 1 out7.3600 XPM110 B
AHenD23R…6e3e6M6c
6341bb927595a7…f750b830819e7a
6 in β†’ 2 out622.4146 XPM969 B
AMv3rJWM…cEC6PPDcAQmjqzoU…5U6sbve9
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.

1.766 Γ— 10⁹⁴(95-digit number)
17660561904326775920…42405122970910722881
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
1.766 Γ— 10⁹⁴(95-digit number)
17660561904326775920…42405122970910722881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.532 Γ— 10⁹⁴(95-digit number)
35321123808653551841…84810245941821445761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.064 Γ— 10⁹⁴(95-digit number)
70642247617307103683…69620491883642891521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.412 Γ— 10⁹⁡(96-digit number)
14128449523461420736…39240983767285783041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.825 Γ— 10⁹⁡(96-digit number)
28256899046922841473…78481967534571566081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.651 Γ— 10⁹⁡(96-digit number)
56513798093845682946…56963935069143132161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.130 Γ— 10⁹⁢(97-digit number)
11302759618769136589…13927870138286264321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.260 Γ— 10⁹⁢(97-digit number)
22605519237538273178…27855740276572528641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.521 Γ— 10⁹⁢(97-digit number)
45211038475076546357…55711480553145057281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.042 Γ— 10⁹⁢(97-digit number)
90422076950153092715…11422961106290114561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.808 Γ— 10⁹⁷(98-digit number)
18084415390030618543…22845922212580229121
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:57,981,832 XPMΒ·at block #6,842,179 Β· updates every 60s
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