Block #922,355

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 10:08:22 AM · Difficulty 10.9155 · 5,887,101 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ff7c2263e10ed388c455f02c26d4f79a778846c7573dfb96842f4423c6cd0289

Height

#922,355

Difficulty

10.915536

Transactions

5

Size

116.01 KB

Version

2

Bits

0aea608c

Nonce

146,079,302

Timestamp

2/4/2015, 10:08:22 AM

Confirmations

5,887,101

Merkle Root

d0bc681fcf43ecab4d17ff715cd922bbb053479c1edddf32e63d8e09e510c62e
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out959.8662 XPM28.97 KB
200 in → 1 out955.3758 XPM28.95 KB
200 in → 1 out1040.1375 XPM28.95 KB
200 in → 1 out992.4646 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.

6.632 × 10⁹⁵(96-digit number)
66329294036131654144…66118675563078609921
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
6.632 × 10⁹⁵(96-digit number)
66329294036131654144…66118675563078609921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.326 × 10⁹⁶(97-digit number)
13265858807226330828…32237351126157219841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.653 × 10⁹⁶(97-digit number)
26531717614452661657…64474702252314439681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.306 × 10⁹⁶(97-digit number)
53063435228905323315…28949404504628879361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.061 × 10⁹⁷(98-digit number)
10612687045781064663…57898809009257758721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.122 × 10⁹⁷(98-digit number)
21225374091562129326…15797618018515517441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.245 × 10⁹⁷(98-digit number)
42450748183124258652…31595236037031034881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.490 × 10⁹⁷(98-digit number)
84901496366248517304…63190472074062069761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.698 × 10⁹⁸(99-digit number)
16980299273249703460…26380944148124139521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.396 × 10⁹⁸(99-digit number)
33960598546499406921…52761888296248279041
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:57,719,719 XPM·at block #6,809,455 · updates every 60s
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