Block #2,240,430

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 8/7/2017, 3:57:17 AM · Difficulty 10.9464 · 4,600,542 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cf167698dc35b16fb4a33b6c0404e6e6b7d4bd2b82420240e2810ed8d8d693de

Height

#2,240,430

Difficulty

10.946442

Transactions

5

Size

1.30 KB

Version

2

Bits

0af24a0c

Nonce

1,022,843,565

Timestamp

8/7/2017, 3:57:17 AM

Confirmations

4,600,542

Merkle Root

930ce8c17051185ce53d23488f702c71d00e8fd5e812db1c9962dfc4c1e660fe
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.

2.134 × 10⁹³(94-digit number)
21345299380576786383…41056206909365750559
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
2.134 × 10⁹³(94-digit number)
21345299380576786383…41056206909365750559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.269 × 10⁹³(94-digit number)
42690598761153572767…82112413818731501119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.538 × 10⁹³(94-digit number)
85381197522307145534…64224827637463002239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.707 × 10⁹⁴(95-digit number)
17076239504461429106…28449655274926004479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.415 × 10⁹⁴(95-digit number)
34152479008922858213…56899310549852008959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.830 × 10⁹⁴(95-digit number)
68304958017845716427…13798621099704017919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.366 × 10⁹⁵(96-digit number)
13660991603569143285…27597242199408035839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.732 × 10⁹⁵(96-digit number)
27321983207138286570…55194484398816071679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.464 × 10⁹⁵(96-digit number)
54643966414276573141…10388968797632143359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.092 × 10⁹⁶(97-digit number)
10928793282855314628…20777937595264286719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.185 × 10⁹⁶(97-digit number)
21857586565710629256…41555875190528573439
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:57,972,134 XPM·at block #6,840,971 · updates every 60s
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