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Block #3,039,616

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/5/2019, 7:43:19 AM Β· Difficulty 11.0189 Β· 3,799,630 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d5fca9c8492c94ff7fc85b09a0930296de99ab8ff26be94d8fce07701477e90d
View on Chainz β†—

Height

#3,039,616

Difficulty

11.018855

Transactions

2

Size

1.72 KB

Version

2

Bits

0b04d3a8

Nonce

1,122,095,554

Timestamp

2/5/2019, 7:43:19 AM

Confirmations

3,799,630

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

f0db45e35748aee1e79eb949e101db56cbaaeee58429fc31bd082e673100e161
Transactions (2)
Coinbasef42f70df791b4d…ce7356ed57bb6c
1 in β†’ 1 out8.2500 XPM110 B
AbXwmGxD…4XXYP765
19dbfe1277b197…80ac5584be4a1c
10 in β†’ 2 out2300.0100 XPM1.52 KB
AG9YhBWB…hb2MctuKAGcsiX1q…ga8Mr9FZ
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.

1.674 Γ— 10⁹⁷(98-digit number)
16742511111872391875…16367830136984304641
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
1.674 Γ— 10⁹⁷(98-digit number)
16742511111872391875…16367830136984304641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.348 Γ— 10⁹⁷(98-digit number)
33485022223744783750…32735660273968609281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.697 Γ— 10⁹⁷(98-digit number)
66970044447489567501…65471320547937218561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.339 Γ— 10⁹⁸(99-digit number)
13394008889497913500…30942641095874437121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.678 Γ— 10⁹⁸(99-digit number)
26788017778995827000…61885282191748874241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.357 Γ— 10⁹⁸(99-digit number)
53576035557991654000…23770564383497748481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.071 Γ— 10⁹⁹(100-digit number)
10715207111598330800…47541128766995496961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.143 Γ— 10⁹⁹(100-digit number)
21430414223196661600…95082257533990993921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.286 Γ— 10⁹⁹(100-digit number)
42860828446393323200…90164515067981987841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.572 Γ— 10⁹⁹(100-digit number)
85721656892786646401…80329030135963975681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.714 Γ— 10¹⁰⁰(101-digit number)
17144331378557329280…60658060271927951361
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:57,958,251 XPMΒ·at block #6,839,245 Β· updates every 60s
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