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Block #2,929,932

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/19/2018, 11:15:59 AM Β· Difficulty 11.3895 Β· 3,909,799 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
75a037bea8bbbcb786f6b80afdb629d8cb69c3c23cd06e6902e7345fdf26e5ae
View on Chainz β†—

Height

#2,929,932

Difficulty

11.389464

Transactions

1

Size

199 B

Version

2

Bits

0b63b3e5

Nonce

1,234,423,931

Timestamp

11/19/2018, 11:15:59 AM

Confirmations

3,909,799

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

dc0b1601da62693acb95133d69e8d437d08717cf811ea1f08c0578575dc65391
Transactions (1)
Coinbasedc0b1601da6269…0578575dc65391
1 in β†’ 1 out7.7000 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.

2.099 Γ— 10⁹²(93-digit number)
20996735613110156296…95540222567160596601
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
2.099 Γ— 10⁹²(93-digit number)
20996735613110156296…95540222567160596601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.199 Γ— 10⁹²(93-digit number)
41993471226220312593…91080445134321193201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.398 Γ— 10⁹²(93-digit number)
83986942452440625187…82160890268642386401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.679 Γ— 10⁹³(94-digit number)
16797388490488125037…64321780537284772801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.359 Γ— 10⁹³(94-digit number)
33594776980976250075…28643561074569545601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.718 Γ— 10⁹³(94-digit number)
67189553961952500150…57287122149139091201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.343 Γ— 10⁹⁴(95-digit number)
13437910792390500030…14574244298278182401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.687 Γ— 10⁹⁴(95-digit number)
26875821584781000060…29148488596556364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.375 Γ— 10⁹⁴(95-digit number)
53751643169562000120…58296977193112729601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.075 Γ— 10⁹⁡(96-digit number)
10750328633912400024…16593954386225459201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.150 Γ— 10⁹⁡(96-digit number)
21500657267824800048…33187908772450918401
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:57,962,133 XPMΒ·at block #6,839,730 Β· updates every 60s
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