Block #1,569,550

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/3/2016, 2:05:00 AM · Difficulty 10.7549 · 5,247,564 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
be9c646927530b04c4f8d89a2e0c674f87a5282df43824b2c082eb2c00e96735

Height

#1,569,550

Difficulty

10.754900

Transactions

2

Size

1.01 KB

Version

2

Bits

0ac1411e

Nonce

878,277,541

Timestamp

5/3/2016, 2:05:00 AM

Confirmations

5,247,564

Merkle Root

d5e703b7acc1b06f67d6880f334d37c6753916989b501f4469482966018639d4
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.

5.449 × 10⁹⁴(95-digit number)
54499701981918404152…39526579434007179921
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
5.449 × 10⁹⁴(95-digit number)
54499701981918404152…39526579434007179921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.089 × 10⁹⁵(96-digit number)
10899940396383680830…79053158868014359841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.179 × 10⁹⁵(96-digit number)
21799880792767361661…58106317736028719681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.359 × 10⁹⁵(96-digit number)
43599761585534723322…16212635472057439361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.719 × 10⁹⁵(96-digit number)
87199523171069446644…32425270944114878721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.743 × 10⁹⁶(97-digit number)
17439904634213889328…64850541888229757441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.487 × 10⁹⁶(97-digit number)
34879809268427778657…29701083776459514881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.975 × 10⁹⁶(97-digit number)
69759618536855557315…59402167552919029761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.395 × 10⁹⁷(98-digit number)
13951923707371111463…18804335105838059521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.790 × 10⁹⁷(98-digit number)
27903847414742222926…37608670211676119041
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:57,780,952 XPM·at block #6,817,113 · updates every 60s
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