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Block #2,510,042

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/7/2018, 2:09:39 PM Β· Difficulty 10.9792 Β· 4,332,882 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a76fc70124f9506e8a7bf9d8bcb7a0e32186718070ae2891c5e7f812bbb55413
View on Chainz β†—

Height

#2,510,042

Difficulty

10.979217

Transactions

2

Size

722 B

Version

2

Bits

0afaadfc

Nonce

689,849,953

Timestamp

2/7/2018, 2:09:39 PM

Confirmations

4,332,882

Mined by

⛏️ P2SHAHk3NeDUEvDPVMzmYBFdFo7E1VRoPpR9oi

Merkle Root

f6f5bc38b5f9c5ee6999e9efa48a595193f98ea52834c45f87e060d49a52eb34
Transactions (2)
Coinbase116223f4f985b1…56a08b0fb4aa61
1 in β†’ 1 out8.2900 XPM110 B
AHk3NeDU…RoPpR9oi
3d81b90e648a69…0114f723d35b3a
3 in β†’ 2 out14.9355 XPM523 B
AKc39hVX…7bmt7o94AGoDaFyf…4E3eYcTg
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.

1.553 Γ— 10⁹²(93-digit number)
15537880835141699852…98616359450113974161
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
1.553 Γ— 10⁹²(93-digit number)
15537880835141699852…98616359450113974161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.107 Γ— 10⁹²(93-digit number)
31075761670283399705…97232718900227948321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.215 Γ— 10⁹²(93-digit number)
62151523340566799411…94465437800455896641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.243 Γ— 10⁹³(94-digit number)
12430304668113359882…88930875600911793281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.486 Γ— 10⁹³(94-digit number)
24860609336226719764…77861751201823586561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.972 Γ— 10⁹³(94-digit number)
49721218672453439529…55723502403647173121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.944 Γ— 10⁹³(94-digit number)
99442437344906879058…11447004807294346241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.988 Γ— 10⁹⁴(95-digit number)
19888487468981375811…22894009614588692481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.977 Γ— 10⁹⁴(95-digit number)
39776974937962751623…45788019229177384961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.955 Γ— 10⁹⁴(95-digit number)
79553949875925503247…91576038458354769921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.591 Γ— 10⁹⁡(96-digit number)
15910789975185100649…83152076916709539841
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:57,987,740 XPMΒ·at block #6,842,923 Β· updates every 60s
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