Block #922,426

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 11:30:39 AM · Difficulty 10.9154 · 5,881,201 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
af078f4830da212320578da452b8ced040d6bb62f0519d5ae98ca48d8ce0f46b

Height

#922,426

Difficulty

10.915379

Transactions

5

Size

116.02 KB

Version

2

Bits

0aea5643

Nonce

355,849,405

Timestamp

2/4/2015, 11:30:39 AM

Confirmations

5,881,201

Merkle Root

d1a8dc5df43e8cb77227637f0647806d1cd79643f422250abef745b81d5e78da
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out952.8935 XPM28.96 KB
200 in → 1 out1045.4561 XPM28.95 KB
200 in → 1 out928.8274 XPM28.95 KB
200 in → 1 out1003.0153 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.

7.231 × 10⁹⁵(96-digit number)
72317856705016135215…18488620324152192159
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
7.231 × 10⁹⁵(96-digit number)
72317856705016135215…18488620324152192159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.446 × 10⁹⁶(97-digit number)
14463571341003227043…36977240648304384319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.892 × 10⁹⁶(97-digit number)
28927142682006454086…73954481296608768639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.785 × 10⁹⁶(97-digit number)
57854285364012908172…47908962593217537279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.157 × 10⁹⁷(98-digit number)
11570857072802581634…95817925186435074559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.314 × 10⁹⁷(98-digit number)
23141714145605163268…91635850372870149119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.628 × 10⁹⁷(98-digit number)
46283428291210326537…83271700745740298239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.256 × 10⁹⁷(98-digit number)
92566856582420653075…66543401491480596479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.851 × 10⁹⁸(99-digit number)
18513371316484130615…33086802982961192959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.702 × 10⁹⁸(99-digit number)
37026742632968261230…66173605965922385919
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:57,673,048 XPM·at block #6,803,626 · updates every 60s
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