Block #922,288

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 8:47:38 AM · Difficulty 10.9158 · 5,872,049 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
620028cec75bb026ed7193b33d0d789a57934256405d32baa25047deb6bd8ae7

Height

#922,288

Difficulty

10.915762

Transactions

5

Size

116.00 KB

Version

2

Bits

0aea6f61

Nonce

191,776,098

Timestamp

2/4/2015, 8:47:38 AM

Confirmations

5,872,049

Merkle Root

3da59a16c57fb9b3385feebfa208aa7a02658f3c9269422bf96dd6e219cf4f6f
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1086.5785 XPM28.96 KB
200 in → 1 out1071.6246 XPM28.95 KB
200 in → 1 out982.7757 XPM28.95 KB
200 in → 1 out1119.7725 XPM28.95 KB
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.

1.763 × 10⁹⁷(98-digit number)
17633710526534320281…36269621383429847041
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
1.763 × 10⁹⁷(98-digit number)
17633710526534320281…36269621383429847041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.526 × 10⁹⁷(98-digit number)
35267421053068640562…72539242766859694081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.053 × 10⁹⁷(98-digit number)
70534842106137281125…45078485533719388161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.410 × 10⁹⁸(99-digit number)
14106968421227456225…90156971067438776321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.821 × 10⁹⁸(99-digit number)
28213936842454912450…80313942134877552641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.642 × 10⁹⁸(99-digit number)
56427873684909824900…60627884269755105281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.128 × 10⁹⁹(100-digit number)
11285574736981964980…21255768539510210561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.257 × 10⁹⁹(100-digit number)
22571149473963929960…42511537079020421121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.514 × 10⁹⁹(100-digit number)
45142298947927859920…85023074158040842241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.028 × 10⁹⁹(100-digit number)
90284597895855719840…70046148316081684481
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:57,598,729 XPM·at block #6,794,336 · updates every 60s
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