Block #1,448,720

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/9/2016, 2:03:11 AM · Difficulty 10.7575 · 5,388,122 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
78b133c3a2d868810072c4778b883c755c7d7b42609836a1cf86d711f9f74860

Height

#1,448,720

Difficulty

10.757468

Transactions

2

Size

866 B

Version

2

Bits

0ac1e972

Nonce

225,641,918

Timestamp

2/9/2016, 2:03:11 AM

Confirmations

5,388,122

Merkle Root

f5fac4d0264c575aded7ef01503b0e4a42fbcbb54f03aab4e3256712b13510de
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.

1.640 × 10⁹²(93-digit number)
16401861765655310555…39994236391040814719
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
1.640 × 10⁹²(93-digit number)
16401861765655310555…39994236391040814719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.280 × 10⁹²(93-digit number)
32803723531310621110…79988472782081629439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.560 × 10⁹²(93-digit number)
65607447062621242221…59976945564163258879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.312 × 10⁹³(94-digit number)
13121489412524248444…19953891128326517759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.624 × 10⁹³(94-digit number)
26242978825048496888…39907782256653035519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.248 × 10⁹³(94-digit number)
52485957650096993777…79815564513306071039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.049 × 10⁹⁴(95-digit number)
10497191530019398755…59631129026612142079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.099 × 10⁹⁴(95-digit number)
20994383060038797510…19262258053224284159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.198 × 10⁹⁴(95-digit number)
41988766120077595021…38524516106448568319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.397 × 10⁹⁴(95-digit number)
83977532240155190043…77049032212897136639
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:57,939,024 XPM·at block #6,836,841 · updates every 60s
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