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Block #2,130,048

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2017, 4:08:19 AM Β· Difficulty 10.9094 Β· 4,712,909 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
026aeecf519cca72c0ed5f2ca77da565091cdd91b62524f5df9eaeb75489b857
View on Chainz β†—

Height

#2,130,048

Difficulty

10.909448

Transactions

2

Size

424 B

Version

2

Bits

0ae8d195

Nonce

193,531,182

Timestamp

5/24/2017, 4:08:19 AM

Confirmations

4,712,909

Mined by

⛏️ P2SHAM47QzPxZDy4tDZXwEU9zTywQDjpCqYe3A

Merkle Root

aa12f8164c90b57629707a588316b9e10e848e71cca23855b2fd91da5417b8f7
Transactions (2)
Coinbase6054a7f7e0aa30…ca566df2673db2
1 in β†’ 1 out8.4000 XPM109 B
AM47QzPx…jpCqYe3A
f5321688deb6af…ab275f09497ee8
1 in β†’ 2 out181324.3844 XPM225 B
ALaG39Nk…33xdQnEmASAMqF9Z…GEi7adhA
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.

2.554 Γ— 10⁹⁡(96-digit number)
25549443183556780038…53554115295931466361
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
2.554 Γ— 10⁹⁡(96-digit number)
25549443183556780038…53554115295931466361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.109 Γ— 10⁹⁡(96-digit number)
51098886367113560077…07108230591862932721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.021 Γ— 10⁹⁢(97-digit number)
10219777273422712015…14216461183725865441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.043 Γ— 10⁹⁢(97-digit number)
20439554546845424031…28432922367451730881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.087 Γ— 10⁹⁢(97-digit number)
40879109093690848062…56865844734903461761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.175 Γ— 10⁹⁢(97-digit number)
81758218187381696124…13731689469806923521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.635 Γ— 10⁹⁷(98-digit number)
16351643637476339224…27463378939613847041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.270 Γ— 10⁹⁷(98-digit number)
32703287274952678449…54926757879227694081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.540 Γ— 10⁹⁷(98-digit number)
65406574549905356899…09853515758455388161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.308 Γ— 10⁹⁸(99-digit number)
13081314909981071379…19707031516910776321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.616 Γ— 10⁹⁸(99-digit number)
26162629819962142759…39414063033821552641
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:57,988,009 XPMΒ·at block #6,842,956 Β· updates every 60s
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