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Block #3,015,388

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/18/2019, 9:06:57 PM Β· Difficulty 11.1763 Β· 3,810,978 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
157419814439a74948ddc425818e9d59e08a4a4f9fddd7c02165dcced0d45dd7
View on Chainz β†—

Height

#3,015,388

Difficulty

11.176297

Transactions

1

Size

200 B

Version

2

Bits

0b2d21d3

Nonce

1,058,286,629

Timestamp

1/18/2019, 9:06:57 PM

Confirmations

3,810,978

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

571b108c22f719fad3267b6c3c48df5fd315af0b2a9395a0d2bc837c3e7aee64
Transactions (1)
Coinbase571b108c22f719…bc837c3e7aee64
1 in β†’ 1 out7.9900 XPM110 B
AUMQRepm…tAfKmdW1
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.

8.191 Γ— 10⁹⁴(95-digit number)
81912445306646534742…90817305248235834441
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
8.191 Γ— 10⁹⁴(95-digit number)
81912445306646534742…90817305248235834441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.638 Γ— 10⁹⁡(96-digit number)
16382489061329306948…81634610496471668881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.276 Γ— 10⁹⁡(96-digit number)
32764978122658613897…63269220992943337761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.552 Γ— 10⁹⁡(96-digit number)
65529956245317227794…26538441985886675521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.310 Γ— 10⁹⁢(97-digit number)
13105991249063445558…53076883971773351041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.621 Γ— 10⁹⁢(97-digit number)
26211982498126891117…06153767943546702081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.242 Γ— 10⁹⁢(97-digit number)
52423964996253782235…12307535887093404161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.048 Γ— 10⁹⁷(98-digit number)
10484792999250756447…24615071774186808321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.096 Γ— 10⁹⁷(98-digit number)
20969585998501512894…49230143548373616641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.193 Γ— 10⁹⁷(98-digit number)
41939171997003025788…98460287096747233281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.387 Γ— 10⁹⁷(98-digit number)
83878343994006051576…96920574193494466561
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:57,855,072 XPMΒ·at block #6,826,365 Β· updates every 60s
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