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Block #2,768,502

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/28/2018, 4:26:21 AM Β· Difficulty 11.6670 Β· 4,073,801 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a4cce3260e55ecef8fea539ccf85309d113df8166e1fd4aa0c73f2836f32f377
View on Chainz β†—

Height

#2,768,502

Difficulty

11.667044

Transactions

1

Size

199 B

Version

2

Bits

0baac367

Nonce

870,305,644

Timestamp

7/28/2018, 4:26:21 AM

Confirmations

4,073,801

Mined by

⛏️ P2SHASRAfaubPkKGRFdAkCqvrnr7QZ3nFrP4ur

Merkle Root

67fd8e0d3df4f080eb46e705a4b8c532d0cefa2eab8fdae08a2090222c5537e7
Transactions (1)
Coinbase67fd8e0d3df4f0…2090222c5537e7
1 in β†’ 1 out7.3300 XPM109 B
ASRAfaub…3nFrP4ur
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.

1.010 Γ— 10⁹⁡(96-digit number)
10104622376808734835…70820431734489234401
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
1.010 Γ— 10⁹⁡(96-digit number)
10104622376808734835…70820431734489234401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.020 Γ— 10⁹⁡(96-digit number)
20209244753617469670…41640863468978468801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.041 Γ— 10⁹⁡(96-digit number)
40418489507234939340…83281726937956937601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.083 Γ— 10⁹⁡(96-digit number)
80836979014469878680…66563453875913875201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.616 Γ— 10⁹⁢(97-digit number)
16167395802893975736…33126907751827750401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.233 Γ— 10⁹⁢(97-digit number)
32334791605787951472…66253815503655500801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.466 Γ— 10⁹⁢(97-digit number)
64669583211575902944…32507631007311001601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.293 Γ— 10⁹⁷(98-digit number)
12933916642315180588…65015262014622003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.586 Γ— 10⁹⁷(98-digit number)
25867833284630361177…30030524029244006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.173 Γ— 10⁹⁷(98-digit number)
51735666569260722355…60061048058488012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.034 Γ— 10⁹⁸(99-digit number)
10347133313852144471…20122096116976025601
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:57,982,829 XPMΒ·at block #6,842,302 Β· updates every 60s
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