Block #1,450,961

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/10/2016, 7:50:52 PM · Difficulty 10.7444 · 5,361,583 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
646d0df01aa43e6017065f0aea6269d7338353f2b06642232bf37699589746ee

Height

#1,450,961

Difficulty

10.744355

Transactions

2

Size

424 B

Version

2

Bits

0abe8e09

Nonce

107,734,666

Timestamp

2/10/2016, 7:50:52 PM

Confirmations

5,361,583

Merkle Root

a45bba4a28432c668fe85f821ded3b68e2a2ad83a19aed495b97db36fd0027b4
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.

1.280 × 10⁹³(94-digit number)
12803321527622475444…83187588044482443979
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
1.280 × 10⁹³(94-digit number)
12803321527622475444…83187588044482443979
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.560 × 10⁹³(94-digit number)
25606643055244950889…66375176088964887959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.121 × 10⁹³(94-digit number)
51213286110489901778…32750352177929775919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.024 × 10⁹⁴(95-digit number)
10242657222097980355…65500704355859551839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.048 × 10⁹⁴(95-digit number)
20485314444195960711…31001408711719103679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.097 × 10⁹⁴(95-digit number)
40970628888391921422…62002817423438207359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.194 × 10⁹⁴(95-digit number)
81941257776783842845…24005634846876414719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.638 × 10⁹⁵(96-digit number)
16388251555356768569…48011269693752829439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.277 × 10⁹⁵(96-digit number)
32776503110713537138…96022539387505658879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.555 × 10⁹⁵(96-digit number)
65553006221427074276…92045078775011317759
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:57,744,383 XPM·at block #6,812,543 · updates every 60s
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