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Block #108,812

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/10/2013, 4:40:31 AM Β· Difficulty 9.6579 Β· 6,702,128 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ebdd1bc6ba6624cbc0cf9ccd75976da4b3d4f6d5316cae258b3bd2481624261d
View on Chainz β†—

Height

#108,812

Difficulty

9.657918

Transactions

1

Size

200 B

Version

2

Bits

09a86d52

Nonce

91,709

Timestamp

8/10/2013, 4:40:31 AM

Confirmations

6,702,128

Mined by

⛏️ P2SHAVN5TcQu993EfviCkpQSYHiBxtuDJ9ZxKG

Merkle Root

b866fe325fbd412ea7516e4cc0d3bb694a9a4dc00cfdb0f16d12dd34d758c4f5
Transactions (1)
Coinbaseb866fe325fbd41…12dd34d758c4f5
1 in β†’ 1 out10.7100 XPM109 B
AVN5TcQu…uDJ9ZxKG
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.

4.358 Γ— 10⁹⁷(98-digit number)
43585066904357068571…00047755856015429701
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
4.358 Γ— 10⁹⁷(98-digit number)
43585066904357068571…00047755856015429701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.717 Γ— 10⁹⁷(98-digit number)
87170133808714137143…00095511712030859401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.743 Γ— 10⁹⁸(99-digit number)
17434026761742827428…00191023424061718801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.486 Γ— 10⁹⁸(99-digit number)
34868053523485654857…00382046848123437601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.973 Γ— 10⁹⁸(99-digit number)
69736107046971309714…00764093696246875201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.394 Γ— 10⁹⁹(100-digit number)
13947221409394261942…01528187392493750401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.789 Γ— 10⁹⁹(100-digit number)
27894442818788523885…03056374784987500801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.578 Γ— 10⁹⁹(100-digit number)
55788885637577047771…06112749569975001601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.115 Γ— 10¹⁰⁰(101-digit number)
11157777127515409554…12225499139950003201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,731,617 XPMΒ·at block #6,810,939 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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