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Block #2,635,120

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 3:31:32 AM Β· Difficulty 11.2932 Β· 4,196,708 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
80548cb029008b9c2174834595de4fe601453be5e57ad1e46e2fb723cd5cd6c0
View on Chainz β†—

Height

#2,635,120

Difficulty

11.293181

Transactions

1

Size

200 B

Version

2

Bits

0b4b0dee

Nonce

576,828,238

Timestamp

4/29/2018, 3:31:32 AM

Confirmations

4,196,708

Mined by

⛏️ P2SHASuTJS8a2X2P33pq6NtxMGfqPxcP7ZUBxw

Merkle Root

8d7b68d71c87f73cbb026cca1b88e651d75cf8999ab48f63c12b977b661b6f4a
Transactions (1)
Coinbase8d7b68d71c87f7…2b977b661b6f4a
1 in β†’ 1 out7.8300 XPM110 B
ASuTJS8a…cP7ZUBxw
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.

1.359 Γ— 10⁹⁡(96-digit number)
13595540208963124110…19540921274623690241
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
1.359 Γ— 10⁹⁡(96-digit number)
13595540208963124110…19540921274623690241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.719 Γ— 10⁹⁡(96-digit number)
27191080417926248221…39081842549247380481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.438 Γ— 10⁹⁡(96-digit number)
54382160835852496442…78163685098494760961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.087 Γ— 10⁹⁢(97-digit number)
10876432167170499288…56327370196989521921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.175 Γ— 10⁹⁢(97-digit number)
21752864334340998576…12654740393979043841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.350 Γ— 10⁹⁢(97-digit number)
43505728668681997153…25309480787958087681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.701 Γ— 10⁹⁢(97-digit number)
87011457337363994307…50618961575916175361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.740 Γ— 10⁹⁷(98-digit number)
17402291467472798861…01237923151832350721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.480 Γ— 10⁹⁷(98-digit number)
34804582934945597723…02475846303664701441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.960 Γ— 10⁹⁷(98-digit number)
69609165869891195446…04951692607329402881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.392 Γ— 10⁹⁸(99-digit number)
13921833173978239089…09903385214658805761
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:57,898,742 XPMΒ·at block #6,831,827 Β· updates every 60s
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