Block #922,308

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 9:12:46 AM · Difficulty 10.9157 · 5,881,298 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f7e5893671d4df60c76e8149b7239489b353685ba688c552b3155f754158ae14

Height

#922,308

Difficulty

10.915675

Transactions

5

Size

115.99 KB

Version

2

Bits

0aea69b5

Nonce

363,484,612

Timestamp

2/4/2015, 9:12:46 AM

Confirmations

5,881,298

Merkle Root

afe055d06bdc6a4603382936193d5b987c6e1f74cbe61b7de4880a23b4deaf0d
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1166.6401 XPM28.97 KB
200 in → 1 out948.7881 XPM28.94 KB
200 in → 1 out1033.8808 XPM28.94 KB
200 in → 1 out1088.0406 XPM28.94 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.

1.318 × 10⁹⁶(97-digit number)
13185982348942058648…37059807038830453761
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
1.318 × 10⁹⁶(97-digit number)
13185982348942058648…37059807038830453761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.637 × 10⁹⁶(97-digit number)
26371964697884117297…74119614077660907521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.274 × 10⁹⁶(97-digit number)
52743929395768234594…48239228155321815041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.054 × 10⁹⁷(98-digit number)
10548785879153646918…96478456310643630081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.109 × 10⁹⁷(98-digit number)
21097571758307293837…92956912621287260161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.219 × 10⁹⁷(98-digit number)
42195143516614587675…85913825242574520321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.439 × 10⁹⁷(98-digit number)
84390287033229175350…71827650485149040641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.687 × 10⁹⁸(99-digit number)
16878057406645835070…43655300970298081281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.375 × 10⁹⁸(99-digit number)
33756114813291670140…87310601940596162561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.751 × 10⁹⁸(99-digit number)
67512229626583340280…74621203881192325121
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:57,672,887 XPM·at block #6,803,605 · updates every 60s
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