Block #377,286

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2014, 12:17:57 AM · Difficulty 10.4233 · 6,437,656 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
428213abf3aaad97f0dbbefddfb4400b3688887ccf2cbf539d41623f4cde9084

Height

#377,286

Difficulty

10.423283

Transactions

4

Size

2.16 KB

Version

2

Bits

0a6c5c3e

Nonce

69,041

Timestamp

1/27/2014, 12:17:57 AM

Confirmations

6,437,656

Merkle Root

4d0363c1a7c60880a5767a18c1f3c1386495621dc540234a297f74413f8ee245
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.

9.740 × 10⁹⁸(99-digit number)
97406290756951667743…04090997161663104001
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
9.740 × 10⁹⁸(99-digit number)
97406290756951667743…04090997161663104001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.948 × 10⁹⁹(100-digit number)
19481258151390333548…08181994323326208001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.896 × 10⁹⁹(100-digit number)
38962516302780667097…16363988646652416001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.792 × 10⁹⁹(100-digit number)
77925032605561334194…32727977293304832001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.558 × 10¹⁰⁰(101-digit number)
15585006521112266838…65455954586609664001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.117 × 10¹⁰⁰(101-digit number)
31170013042224533677…30911909173219328001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.234 × 10¹⁰⁰(101-digit number)
62340026084449067355…61823818346438656001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.246 × 10¹⁰¹(102-digit number)
12468005216889813471…23647636692877312001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.493 × 10¹⁰¹(102-digit number)
24936010433779626942…47295273385754624001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.987 × 10¹⁰¹(102-digit number)
49872020867559253884…94590546771509248001
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:57,763,632 XPM·at block #6,814,941 · updates every 60s
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