Block #454,655

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/22/2014, 2:26:44 AM · Difficulty 10.3967 · 6,355,530 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7744603bfc72ad40857699e360ffdffbc45f6c3efd773110f96942484298692d

Height

#454,655

Difficulty

10.396651

Transactions

2

Size

434 B

Version

2

Bits

0a658af1

Nonce

103,001

Timestamp

3/22/2014, 2:26:44 AM

Confirmations

6,355,530

Merkle Root

45ce9f560b5c85e97ee2af39479ec910cb8996c662f77a3ffd14d2e55fdb0c1b
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.

4.026 × 10¹⁰⁰(101-digit number)
40264456605679465594…39504320717624788481
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
4.026 × 10¹⁰⁰(101-digit number)
40264456605679465594…39504320717624788481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.052 × 10¹⁰⁰(101-digit number)
80528913211358931189…79008641435249576961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.610 × 10¹⁰¹(102-digit number)
16105782642271786237…58017282870499153921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.221 × 10¹⁰¹(102-digit number)
32211565284543572475…16034565740998307841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.442 × 10¹⁰¹(102-digit number)
64423130569087144951…32069131481996615681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.288 × 10¹⁰²(103-digit number)
12884626113817428990…64138262963993231361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.576 × 10¹⁰²(103-digit number)
25769252227634857980…28276525927986462721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.153 × 10¹⁰²(103-digit number)
51538504455269715961…56553051855972925441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.030 × 10¹⁰³(104-digit number)
10307700891053943192…13106103711945850881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.061 × 10¹⁰³(104-digit number)
20615401782107886384…26212207423891701761
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,725,549 XPM·at block #6,810,184 · updates every 60s
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