Block #1,596,698

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/23/2016, 1:28:31 PM · Difficulty 10.6119 · 5,219,791 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0c3364e94d0c848dad06df6896237e1840bed425224b339081ad554892b1f4f8

Height

#1,596,698

Difficulty

10.611888

Transactions

2

Size

2.05 KB

Version

2

Bits

0a9ca4ad

Nonce

242,424,163

Timestamp

5/23/2016, 1:28:31 PM

Confirmations

5,219,791

Merkle Root

e17d3259cad21bff09152cf0c346c5d0f81a2f300ed114f4d14b75fd38f4ae3b
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.

3.755 × 10⁹⁴(95-digit number)
37556090287087437389…16589345936070957661
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
3.755 × 10⁹⁴(95-digit number)
37556090287087437389…16589345936070957661
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.511 × 10⁹⁴(95-digit number)
75112180574174874779…33178691872141915321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.502 × 10⁹⁵(96-digit number)
15022436114834974955…66357383744283830641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.004 × 10⁹⁵(96-digit number)
30044872229669949911…32714767488567661281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.008 × 10⁹⁵(96-digit number)
60089744459339899823…65429534977135322561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.201 × 10⁹⁶(97-digit number)
12017948891867979964…30859069954270645121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.403 × 10⁹⁶(97-digit number)
24035897783735959929…61718139908541290241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.807 × 10⁹⁶(97-digit number)
48071795567471919858…23436279817082580481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.614 × 10⁹⁶(97-digit number)
96143591134943839717…46872559634165160961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.922 × 10⁹⁷(98-digit number)
19228718226988767943…93745119268330321921
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:57,776,039 XPM·at block #6,816,488 · updates every 60s
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