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Block #2,833,437

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 6:10:44 PM Β· Difficulty 11.7153 Β· 4,009,110 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f9ecc55e44eeed4eedd792490903d40216f1c83f171d8c0987b18fcd9b5e7448
View on Chainz β†—

Height

#2,833,437

Difficulty

11.715320

Transactions

3

Size

17.18 KB

Version

2

Bits

0bb71f2f

Nonce

790,921,670

Timestamp

9/10/2018, 6:10:44 PM

Confirmations

4,009,110

Mined by

⛏️ P2SHALZDAYb71dxuhZcDMyMWjWEP3hKLHRxJ3P

Merkle Root

832604aeaad211d3a1c26d20b1e76c579fee9989524988d90e3561e4b4c071e3
Transactions (3)
Coinbased17633693d12da…534813124ddf35
1 in β†’ 1 out7.4600 XPM110 B
ALZDAYb7…KLHRxJ3P
ee8d58f566e910…7ed37a076c54aa
71 in β†’ 2 out500.0100 XPM8.08 KB
AJohFYjg…9b6DukjFAJcDB81D…ZX2on3Cs
8eed11a9bff260…1bc6745e1ccb84
76 in β†’ 1 out500.0000 XPM8.90 KB
APt1Y8pX…UT7nuRWU
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.

1.494 Γ— 10⁹⁴(95-digit number)
14941406095371607965…03720124636822942721
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
1.494 Γ— 10⁹⁴(95-digit number)
14941406095371607965…03720124636822942721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.988 Γ— 10⁹⁴(95-digit number)
29882812190743215930…07440249273645885441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.976 Γ— 10⁹⁴(95-digit number)
59765624381486431860…14880498547291770881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.195 Γ— 10⁹⁡(96-digit number)
11953124876297286372…29760997094583541761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.390 Γ— 10⁹⁡(96-digit number)
23906249752594572744…59521994189167083521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.781 Γ— 10⁹⁡(96-digit number)
47812499505189145488…19043988378334167041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.562 Γ— 10⁹⁡(96-digit number)
95624999010378290977…38087976756668334081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.912 Γ— 10⁹⁢(97-digit number)
19124999802075658195…76175953513336668161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.824 Γ— 10⁹⁢(97-digit number)
38249999604151316390…52351907026673336321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.649 Γ— 10⁹⁢(97-digit number)
76499999208302632781…04703814053346672641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.529 Γ— 10⁹⁷(98-digit number)
15299999841660526556…09407628106693345281
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:57,984,801 XPMΒ·at block #6,842,546 Β· updates every 60s
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