Block #922,461

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 12:11:20 PM · Difficulty 10.9153 · 5,882,552 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5ffe30a94a641818cc66857d3723298f106548affaf036089869630d4dc1a5be

Height

#922,461

Difficulty

10.915274

Transactions

5

Size

116.04 KB

Version

2

Bits

0aea4f6a

Nonce

444,583,737

Timestamp

2/4/2015, 12:11:20 PM

Confirmations

5,882,552

Merkle Root

f4903cc5c1bb3e894b0e0bff5fc0f7c2c1cc3563cd64d22afcd3ea3cc4e4ec29
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1018.3008 XPM28.96 KB
200 in → 1 out984.7098 XPM28.96 KB
200 in → 1 out1084.3796 XPM28.96 KB
200 in → 1 out926.0115 XPM28.96 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.

8.844 × 10⁹⁴(95-digit number)
88448354976223751126…20592844903629980961
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
8.844 × 10⁹⁴(95-digit number)
88448354976223751126…20592844903629980961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.768 × 10⁹⁵(96-digit number)
17689670995244750225…41185689807259961921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.537 × 10⁹⁵(96-digit number)
35379341990489500450…82371379614519923841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.075 × 10⁹⁵(96-digit number)
70758683980979000901…64742759229039847681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.415 × 10⁹⁶(97-digit number)
14151736796195800180…29485518458079695361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.830 × 10⁹⁶(97-digit number)
28303473592391600360…58971036916159390721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.660 × 10⁹⁶(97-digit number)
56606947184783200720…17942073832318781441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.132 × 10⁹⁷(98-digit number)
11321389436956640144…35884147664637562881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.264 × 10⁹⁷(98-digit number)
22642778873913280288…71768295329275125761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.528 × 10⁹⁷(98-digit number)
45285557747826560576…43536590658550251521
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,684,174 XPM·at block #6,805,012 · updates every 60s
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