Block #375,605

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/25/2014, 8:02:56 PM · Difficulty 10.4247 · 6,441,613 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2d7a9f90b4834d18045d04568594ab35e1382ff7e722bda4018c03f70778267d

Height

#375,605

Difficulty

10.424663

Transactions

1

Size

937 B

Version

2

Bits

0a6cb6bf

Nonce

77,231

Timestamp

1/25/2014, 8:02:56 PM

Confirmations

6,441,613

Merkle Root

94240a6fb2d7019c0d38780ecb4aa16c406c10927140284ee6909ac55ced05e9
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.838 × 10⁹⁸(99-digit number)
88382699694881934284…33948478049466539521
Discovered Prime Numbers
p_k = 2^k × 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
8.838 × 10⁹⁸(99-digit number)
88382699694881934284…33948478049466539521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.767 × 10⁹⁹(100-digit number)
17676539938976386856…67896956098933079041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.535 × 10⁹⁹(100-digit number)
35353079877952773713…35793912197866158081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.070 × 10⁹⁹(100-digit number)
70706159755905547427…71587824395732316161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.414 × 10¹⁰⁰(101-digit number)
14141231951181109485…43175648791464632321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.828 × 10¹⁰⁰(101-digit number)
28282463902362218970…86351297582929264641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.656 × 10¹⁰⁰(101-digit number)
56564927804724437941…72702595165858529281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.131 × 10¹⁰¹(102-digit number)
11312985560944887588…45405190331717058561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.262 × 10¹⁰¹(102-digit number)
22625971121889775176…90810380663434117121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.525 × 10¹⁰¹(102-digit number)
45251942243779550353…81620761326868234241
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,781,782 XPM·at block #6,817,217 · updates every 60s
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