Block #922,279

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 8:35:00 AM · Difficulty 10.9158 · 5,883,934 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
73536bee8209e4e14dc7e7c3f50f8eb71f81cb5ecfe3090575d1041e49872bce

Height

#922,279

Difficulty

10.915822

Transactions

5

Size

115.97 KB

Version

2

Bits

0aea734d

Nonce

2,131,306,302

Timestamp

2/4/2015, 8:35:00 AM

Confirmations

5,883,934

Merkle Root

d4ebc8c84dd5327769c99073e9ce81fba8a28c6a12e71ce4a6f9fea3fb8f3a5b
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1072.4268 XPM28.94 KB
200 in → 1 out929.9306 XPM28.94 KB
200 in → 1 out1073.5732 XPM28.94 KB
200 in → 1 out1110.0228 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.

1.092 × 10⁹⁷(98-digit number)
10928323353653512329…32382448304474314239
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
1.092 × 10⁹⁷(98-digit number)
10928323353653512329…32382448304474314239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.185 × 10⁹⁷(98-digit number)
21856646707307024658…64764896608948628479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.371 × 10⁹⁷(98-digit number)
43713293414614049316…29529793217897256959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.742 × 10⁹⁷(98-digit number)
87426586829228098632…59059586435794513919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.748 × 10⁹⁸(99-digit number)
17485317365845619726…18119172871589027839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.497 × 10⁹⁸(99-digit number)
34970634731691239453…36238345743178055679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.994 × 10⁹⁸(99-digit number)
69941269463382478906…72476691486356111359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.398 × 10⁹⁹(100-digit number)
13988253892676495781…44953382972712222719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.797 × 10⁹⁹(100-digit number)
27976507785352991562…89906765945424445439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.595 × 10⁹⁹(100-digit number)
55953015570705983124…79813531890848890879
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,693,783 XPM·at block #6,806,212 · updates every 60s
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