Block #922,318

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 9:27:27 AM · Difficulty 10.9156 · 5,881,262 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5b993748263ef0f27b5fa6333d1c96e84b16cb7eb00be77ea2833b22e0229c40

Height

#922,318

Difficulty

10.915606

Transactions

5

Size

115.98 KB

Version

2

Bits

0aea652c

Nonce

2,135,236,652

Timestamp

2/4/2015, 9:27:27 AM

Confirmations

5,881,262

Merkle Root

411bdee832f5557d0373d7f51a150a2d7ee173ee5e397bb9667f160355ec29eb
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1023.6642 XPM28.95 KB
200 in → 1 out944.9397 XPM28.94 KB
200 in → 1 out868.9940 XPM28.94 KB
200 in → 1 out933.6538 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.

1.111 × 10⁹⁶(97-digit number)
11110682405609083831…00464937050788722959
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
1.111 × 10⁹⁶(97-digit number)
11110682405609083831…00464937050788722959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.222 × 10⁹⁶(97-digit number)
22221364811218167663…00929874101577445919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.444 × 10⁹⁶(97-digit number)
44442729622436335326…01859748203154891839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.888 × 10⁹⁶(97-digit number)
88885459244872670653…03719496406309783679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.777 × 10⁹⁷(98-digit number)
17777091848974534130…07438992812619567359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.555 × 10⁹⁷(98-digit number)
35554183697949068261…14877985625239134719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.110 × 10⁹⁷(98-digit number)
71108367395898136522…29755971250478269439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.422 × 10⁹⁸(99-digit number)
14221673479179627304…59511942500956538879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.844 × 10⁹⁸(99-digit number)
28443346958359254608…19023885001913077759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.688 × 10⁹⁸(99-digit number)
56886693916718509217…38047770003826155519
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:57,672,675 XPM·at block #6,803,579 · updates every 60s
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