Block #922,312

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 9:20:41 AM · Difficulty 10.9157 · 5,873,024 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d573445a6951a9dc241419a479078d5ee15877c9ae0947ad9c19621d9bb59f47

Height

#922,312

Difficulty

10.915676

Transactions

5

Size

115.98 KB

Version

2

Bits

0aea69b7

Nonce

1,935,319,716

Timestamp

2/4/2015, 9:20:41 AM

Confirmations

5,873,024

Merkle Root

9008ebdb4b8f9cc086d3f857dcae083200c5275c99fdd77c0877409a2ead1819
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out995.7559 XPM28.94 KB
200 in → 1 out1034.6674 XPM28.94 KB
200 in → 1 out935.9936 XPM28.94 KB
200 in → 1 out977.7448 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.

3.619 × 10⁹⁷(98-digit number)
36195042468937285781…38857026899619199999
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
3.619 × 10⁹⁷(98-digit number)
36195042468937285781…38857026899619199999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.239 × 10⁹⁷(98-digit number)
72390084937874571562…77714053799238399999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.447 × 10⁹⁸(99-digit number)
14478016987574914312…55428107598476799999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.895 × 10⁹⁸(99-digit number)
28956033975149828624…10856215196953599999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.791 × 10⁹⁸(99-digit number)
57912067950299657249…21712430393907199999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.158 × 10⁹⁹(100-digit number)
11582413590059931449…43424860787814399999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.316 × 10⁹⁹(100-digit number)
23164827180119862899…86849721575628799999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.632 × 10⁹⁹(100-digit number)
46329654360239725799…73699443151257599999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.265 × 10⁹⁹(100-digit number)
92659308720479451599…47398886302515199999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.853 × 10¹⁰⁰(101-digit number)
18531861744095890319…94797772605030399999
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:57,606,746 XPM·at block #6,795,335 · updates every 60s
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