Block #1,426,748

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2016, 8:28:40 PM · Difficulty 10.7548 · 5,414,388 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2fc0980df78cab31a3a0d9a39e9399e1fea5d4ac72f69b84911a47f1f6904bfb

Height

#1,426,748

Difficulty

10.754775

Transactions

2

Size

1.15 KB

Version

2

Bits

0ac138ea

Nonce

229,409,772

Timestamp

1/24/2016, 8:28:40 PM

Confirmations

5,414,388

Merkle Root

c69db1c7e93bb8cb03a36c4267db2cc163d96c74a6212689bdfbf575f7681e4f
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.

2.421 × 10⁹³(94-digit number)
24219056103199460281…34944551738875932721
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
2.421 × 10⁹³(94-digit number)
24219056103199460281…34944551738875932721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.843 × 10⁹³(94-digit number)
48438112206398920563…69889103477751865441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.687 × 10⁹³(94-digit number)
96876224412797841127…39778206955503730881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.937 × 10⁹⁴(95-digit number)
19375244882559568225…79556413911007461761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.875 × 10⁹⁴(95-digit number)
38750489765119136451…59112827822014923521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.750 × 10⁹⁴(95-digit number)
77500979530238272902…18225655644029847041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.550 × 10⁹⁵(96-digit number)
15500195906047654580…36451311288059694081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.100 × 10⁹⁵(96-digit number)
31000391812095309160…72902622576119388161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.200 × 10⁹⁵(96-digit number)
62000783624190618321…45805245152238776321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.240 × 10⁹⁶(97-digit number)
12400156724838123664…91610490304477552641
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:57,973,450 XPM·at block #6,841,135 · updates every 60s
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