Block #922,455

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 12:02:16 PM · Difficulty 10.9153 · 5,871,320 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c1084d373e4617d3851e601486f0932e9953578b3c535c499c5daeaf7c739321

Height

#922,455

Difficulty

10.915309

Transactions

5

Size

116.03 KB

Version

2

Bits

0aea51b7

Nonce

472,657,337

Timestamp

2/4/2015, 12:02:16 PM

Confirmations

5,871,320

Merkle Root

3a0a99df4c265f21c3324ab1aa78907096b7effc955e24a9c7a7adfe142fc4ee
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1095.3022 XPM28.96 KB
200 in → 1 out900.0296 XPM28.96 KB
200 in → 1 out978.6488 XPM28.96 KB
200 in → 1 out993.8252 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.

8.559 × 10⁹⁴(95-digit number)
85598404213156315216…49215533866922147639
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
8.559 × 10⁹⁴(95-digit number)
85598404213156315216…49215533866922147639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.711 × 10⁹⁵(96-digit number)
17119680842631263043…98431067733844295279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.423 × 10⁹⁵(96-digit number)
34239361685262526086…96862135467688590559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.847 × 10⁹⁵(96-digit number)
68478723370525052173…93724270935377181119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.369 × 10⁹⁶(97-digit number)
13695744674105010434…87448541870754362239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.739 × 10⁹⁶(97-digit number)
27391489348210020869…74897083741508724479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.478 × 10⁹⁶(97-digit number)
54782978696420041738…49794167483017448959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.095 × 10⁹⁷(98-digit number)
10956595739284008347…99588334966034897919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.191 × 10⁹⁷(98-digit number)
21913191478568016695…99176669932069795839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.382 × 10⁹⁷(98-digit number)
43826382957136033390…98353339864139591679
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:57,594,204 XPM·at block #6,793,774 · updates every 60s
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