Block #922,389

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 10:45:55 AM · Difficulty 10.9155 · 5,872,754 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e7d247d5842ab81d8799c278b04cbb86a6db328176135221e2f253b8e1a522ed

Height

#922,389

Difficulty

10.915482

Transactions

5

Size

115.99 KB

Version

2

Bits

0aea5d0d

Nonce

741,835,612

Timestamp

2/4/2015, 10:45:55 AM

Confirmations

5,872,754

Merkle Root

a5f9c62e27115896ab93c786c6ccdbea66803839efdf84a02b41b983c2e8d82f
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1205.1787 XPM28.95 KB
200 in → 1 out996.4205 XPM28.95 KB
200 in → 1 out1016.3275 XPM28.95 KB
200 in → 1 out1118.6480 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.

8.666 × 10⁹⁵(96-digit number)
86666234058722209910…91623797050887392719
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
8.666 × 10⁹⁵(96-digit number)
86666234058722209910…91623797050887392719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.733 × 10⁹⁶(97-digit number)
17333246811744441982…83247594101774785439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.466 × 10⁹⁶(97-digit number)
34666493623488883964…66495188203549570879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.933 × 10⁹⁶(97-digit number)
69332987246977767928…32990376407099141759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.386 × 10⁹⁷(98-digit number)
13866597449395553585…65980752814198283519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.773 × 10⁹⁷(98-digit number)
27733194898791107171…31961505628396567039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.546 × 10⁹⁷(98-digit number)
55466389797582214342…63923011256793134079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.109 × 10⁹⁸(99-digit number)
11093277959516442868…27846022513586268159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.218 × 10⁹⁸(99-digit number)
22186555919032885736…55692045027172536319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.437 × 10⁹⁸(99-digit number)
44373111838065771473…11384090054345072639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
8.874 × 10⁹⁸(99-digit number)
88746223676131542947…22768180108690145279
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,605,185 XPM·at block #6,795,142 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.