Block #2,272,260

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/28/2017, 7:04:21 PM · Difficulty 10.9541 · 4,566,493 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f4981e502ea81e3fe58a995b23e71960611a2023aeca0e11a4bcfd35521685cb

Height

#2,272,260

Difficulty

10.954126

Transactions

5

Size

5.07 KB

Version

2

Bits

0af4419f

Nonce

533,234,897

Timestamp

8/28/2017, 7:04:21 PM

Confirmations

4,566,493

Merkle Root

d9647c256751b6129874a72aac10e21f5915337539432bcf7d52914b63c86d31
Transactions (5)
1 in → 1 out8.3900 XPM110 B
4 in → 1 out12.0000 XPM603 B
6 in → 1 out16.0000 XPM898 B
11 in → 1 out4.0000 XPM1.63 KB
12 in → 1 out4.0000 XPM1.78 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.

4.114 × 10⁹³(94-digit number)
41144317814930419973…11849401529320932681
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
4.114 × 10⁹³(94-digit number)
41144317814930419973…11849401529320932681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.228 × 10⁹³(94-digit number)
82288635629860839947…23698803058641865361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.645 × 10⁹⁴(95-digit number)
16457727125972167989…47397606117283730721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.291 × 10⁹⁴(95-digit number)
32915454251944335978…94795212234567461441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.583 × 10⁹⁴(95-digit number)
65830908503888671957…89590424469134922881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.316 × 10⁹⁵(96-digit number)
13166181700777734391…79180848938269845761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.633 × 10⁹⁵(96-digit number)
26332363401555468783…58361697876539691521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.266 × 10⁹⁵(96-digit number)
52664726803110937566…16723395753079383041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.053 × 10⁹⁶(97-digit number)
10532945360622187513…33446791506158766081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.106 × 10⁹⁶(97-digit number)
21065890721244375026…66893583012317532161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.213 × 10⁹⁶(97-digit number)
42131781442488750053…33787166024635064321
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,954,282 XPM·at block #6,838,752 · updates every 60s
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