Block #922,441

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 11:49:56 AM · Difficulty 10.9153 · 5,888,565 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8139c06fd1c0dfb77bac06d608831b43a66b99d6bb405c649020fdd0687ba68d

Height

#922,441

Difficulty

10.915292

Transactions

5

Size

116.03 KB

Version

2

Bits

0aea5095

Nonce

90,334,075

Timestamp

2/4/2015, 11:49:56 AM

Confirmations

5,888,565

Merkle Root

be788883cdabee939cfde1749b298d011d12e86545d02a5cce26baf7fbf9a8c3
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1093.2193 XPM28.96 KB
200 in → 1 out1007.7738 XPM28.96 KB
200 in → 1 out986.5129 XPM28.96 KB
200 in → 1 out1068.0329 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.

6.999 × 10⁹⁷(98-digit number)
69997464685566388676…56768142112686786559
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
6.999 × 10⁹⁷(98-digit number)
69997464685566388676…56768142112686786559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.399 × 10⁹⁸(99-digit number)
13999492937113277735…13536284225373573119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.799 × 10⁹⁸(99-digit number)
27998985874226555470…27072568450747146239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.599 × 10⁹⁸(99-digit number)
55997971748453110941…54145136901494292479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.119 × 10⁹⁹(100-digit number)
11199594349690622188…08290273802988584959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.239 × 10⁹⁹(100-digit number)
22399188699381244376…16580547605977169919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.479 × 10⁹⁹(100-digit number)
44798377398762488752…33161095211954339839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.959 × 10⁹⁹(100-digit number)
89596754797524977505…66322190423908679679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.791 × 10¹⁰⁰(101-digit number)
17919350959504995501…32644380847817359359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.583 × 10¹⁰⁰(101-digit number)
35838701919009991002…65288761695634718719
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:57,732,152 XPM·at block #6,811,005 · updates every 60s
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