Block #1,477,275

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/29/2016, 3:04:18 PM · Difficulty 10.7038 · 5,363,375 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d93f12d39dc4e4887dae7a3cecc31ffde700e4d81ac764833ad48350b7b73635

Height

#1,477,275

Difficulty

10.703831

Transactions

2

Size

1.15 KB

Version

2

Bits

0ab42e44

Nonce

453,480,703

Timestamp

2/29/2016, 3:04:18 PM

Confirmations

5,363,375

Merkle Root

e110767d9dea00a30a26218037f073e7cccb0499c5305990991cf03ca85d178a
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.

9.654 × 10⁹³(94-digit number)
96548318299338969787…05225722128879003411
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
9.654 × 10⁹³(94-digit number)
96548318299338969787…05225722128879003411
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.930 × 10⁹⁴(95-digit number)
19309663659867793957…10451444257758006821
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.861 × 10⁹⁴(95-digit number)
38619327319735587914…20902888515516013641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.723 × 10⁹⁴(95-digit number)
77238654639471175829…41805777031032027281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.544 × 10⁹⁵(96-digit number)
15447730927894235165…83611554062064054561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.089 × 10⁹⁵(96-digit number)
30895461855788470331…67223108124128109121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.179 × 10⁹⁵(96-digit number)
61790923711576940663…34446216248256218241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.235 × 10⁹⁶(97-digit number)
12358184742315388132…68892432496512436481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.471 × 10⁹⁶(97-digit number)
24716369484630776265…37784864993024872961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.943 × 10⁹⁶(97-digit number)
49432738969261552531…75569729986049745921
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:57,969,542 XPM·at block #6,840,649 · updates every 60s
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