Block #922,460

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 12:09:52 PM · Difficulty 10.9153 · 5,870,527 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
da5b0b51172bcdece47b2fa12d35dd2f3091576d69a74c36837133a1d435d420

Height

#922,460

Difficulty

10.915305

Transactions

5

Size

116.03 KB

Version

2

Bits

0aea516e

Nonce

2,234,089,977

Timestamp

2/4/2015, 12:09:52 PM

Confirmations

5,870,527

Merkle Root

9ce699d7b4dbb4d8e045f1bc0cd7971ca50ebbfa77a597d8993b99f524c22a9f
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1081.8207 XPM28.96 KB
200 in → 1 out1029.5124 XPM28.96 KB
200 in → 1 out1001.0812 XPM28.96 KB
200 in → 1 out993.2770 XPM28.96 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.

5.623 × 10⁹⁶(97-digit number)
56232554589143886852…98490041891263862561
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
5.623 × 10⁹⁶(97-digit number)
56232554589143886852…98490041891263862561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.124 × 10⁹⁷(98-digit number)
11246510917828777370…96980083782527725121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.249 × 10⁹⁷(98-digit number)
22493021835657554741…93960167565055450241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.498 × 10⁹⁷(98-digit number)
44986043671315109482…87920335130110900481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.997 × 10⁹⁷(98-digit number)
89972087342630218964…75840670260221800961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.799 × 10⁹⁸(99-digit number)
17994417468526043792…51681340520443601921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.598 × 10⁹⁸(99-digit number)
35988834937052087585…03362681040887203841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.197 × 10⁹⁸(99-digit number)
71977669874104175171…06725362081774407681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.439 × 10⁹⁹(100-digit number)
14395533974820835034…13450724163548815361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.879 × 10⁹⁹(100-digit number)
28791067949641670068…26901448327097630721
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:57,587,878 XPM·at block #6,792,986 · updates every 60s
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