Block #922,282

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 8:40:55 AM · Difficulty 10.9158 · 5,884,419 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
41f67b3c2af843d89f3963578b0439127a7728f34719d8919f5a58b3338200e8

Height

#922,282

Difficulty

10.915799

Transactions

5

Size

116.00 KB

Version

2

Bits

0aea71cf

Nonce

1,031,908,925

Timestamp

2/4/2015, 8:40:55 AM

Confirmations

5,884,419

Merkle Root

7683ccdc26111f428fe77ff202c54b3a2f9b332c39becbb424ab80d6f4ad3878
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1231.7881 XPM28.98 KB
200 in → 1 out902.1823 XPM28.94 KB
200 in → 1 out1033.3299 XPM28.94 KB
200 in → 1 out989.4320 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.

5.713 × 10⁹⁶(97-digit number)
57137928377873911517…33354481364649164799
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
5.713 × 10⁹⁶(97-digit number)
57137928377873911517…33354481364649164799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.142 × 10⁹⁷(98-digit number)
11427585675574782303…66708962729298329599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.285 × 10⁹⁷(98-digit number)
22855171351149564606…33417925458596659199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.571 × 10⁹⁷(98-digit number)
45710342702299129213…66835850917193318399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.142 × 10⁹⁷(98-digit number)
91420685404598258427…33671701834386636799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.828 × 10⁹⁸(99-digit number)
18284137080919651685…67343403668773273599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.656 × 10⁹⁸(99-digit number)
36568274161839303371…34686807337546547199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.313 × 10⁹⁸(99-digit number)
73136548323678606742…69373614675093094399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.462 × 10⁹⁹(100-digit number)
14627309664735721348…38747229350186188799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.925 × 10⁹⁹(100-digit number)
29254619329471442696…77494458700372377599
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:57,697,705 XPM·at block #6,806,700 · updates every 60s
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