Block #2,063,323

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/9/2017, 11:22:04 AM · Difficulty 10.8528 · 4,752,944 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e28bf1908c11b1d16f8eb02e4635d63a4ebd670d70798a32e61f6949a977b095

Height

#2,063,323

Difficulty

10.852754

Transactions

2

Size

424 B

Version

2

Bits

0ada4e19

Nonce

32,733,632

Timestamp

4/9/2017, 11:22:04 AM

Confirmations

4,752,944

Merkle Root

ea10181dba9a054553204e03619b418b4c65988ead481a178eafdb1dcb5f38ff
Transactions (2)
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.

1.124 × 10⁹²(93-digit number)
11243059940809228648…08989402518819489599
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
1.124 × 10⁹²(93-digit number)
11243059940809228648…08989402518819489599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.248 × 10⁹²(93-digit number)
22486119881618457296…17978805037638979199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.497 × 10⁹²(93-digit number)
44972239763236914593…35957610075277958399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.994 × 10⁹²(93-digit number)
89944479526473829186…71915220150555916799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.798 × 10⁹³(94-digit number)
17988895905294765837…43830440301111833599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.597 × 10⁹³(94-digit number)
35977791810589531674…87660880602223667199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.195 × 10⁹³(94-digit number)
71955583621179063349…75321761204447334399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.439 × 10⁹⁴(95-digit number)
14391116724235812669…50643522408894668799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.878 × 10⁹⁴(95-digit number)
28782233448471625339…01287044817789337599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.756 × 10⁹⁴(95-digit number)
57564466896943250679…02574089635578675199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.151 × 10⁹⁵(96-digit number)
11512893379388650135…05148179271157350399
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:57,774,250 XPM·at block #6,816,266 · updates every 60s
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