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Block #2,867,364

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/4/2018, 8:46:58 PM Β· Difficulty 11.6682 Β· 3,972,763 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bf3638f08143e2ad114673ba1baf8f7e0f0b7bb256bf922688c6259983fcf887
View on Chainz β†—

Height

#2,867,364

Difficulty

11.668181

Transactions

1

Size

199 B

Version

2

Bits

0bab0de8

Nonce

933,258,026

Timestamp

10/4/2018, 8:46:58 PM

Confirmations

3,972,763

Mined by

⛏️ P2SHALQGpaT6bUeDR1X73XRmMe4Z6w9dLVU1B9

Merkle Root

f1f9b3a0e00dd781ac8bfa673825b2efff72b7b54fdccb345470db9bde9bcf31
Transactions (1)
Coinbasef1f9b3a0e00dd7…70db9bde9bcf31
1 in β†’ 1 out7.3300 XPM109 B
ALQGpaT6…9dLVU1B9
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.

4.248 Γ— 10⁹⁡(96-digit number)
42485068908651165932…04455985478875615681
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
4.248 Γ— 10⁹⁡(96-digit number)
42485068908651165932…04455985478875615681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.497 Γ— 10⁹⁡(96-digit number)
84970137817302331864…08911970957751231361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.699 Γ— 10⁹⁢(97-digit number)
16994027563460466372…17823941915502462721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.398 Γ— 10⁹⁢(97-digit number)
33988055126920932745…35647883831004925441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.797 Γ— 10⁹⁢(97-digit number)
67976110253841865491…71295767662009850881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.359 Γ— 10⁹⁷(98-digit number)
13595222050768373098…42591535324019701761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.719 Γ— 10⁹⁷(98-digit number)
27190444101536746196…85183070648039403521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.438 Γ— 10⁹⁷(98-digit number)
54380888203073492393…70366141296078807041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.087 Γ— 10⁹⁸(99-digit number)
10876177640614698478…40732282592157614081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.175 Γ— 10⁹⁸(99-digit number)
21752355281229396957…81464565184315228161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.350 Γ— 10⁹⁸(99-digit number)
43504710562458793914…62929130368630456321
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:57,965,330 XPMΒ·at block #6,840,126 Β· updates every 60s
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