Block #373,368

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/24/2014, 6:32:58 AM · Difficulty 10.4252 · 6,444,636 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
75f52a439eb4ae53ffb54009c343b0cf2087401d72e7230e55d83ccc96fd15ce

Height

#373,368

Difficulty

10.425231

Transactions

2

Size

582 B

Version

2

Bits

0a6cdbef

Nonce

35,508

Timestamp

1/24/2014, 6:32:58 AM

Confirmations

6,444,636

Merkle Root

caa749a1686765a7dba297a4f21edc167f06ee296acb5a8f654787c73f3b9b89
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.

2.084 × 10⁹⁹(100-digit number)
20840401512071196217…33867567736783516159
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
2.084 × 10⁹⁹(100-digit number)
20840401512071196217…33867567736783516159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.168 × 10⁹⁹(100-digit number)
41680803024142392435…67735135473567032319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.336 × 10⁹⁹(100-digit number)
83361606048284784871…35470270947134064639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.667 × 10¹⁰⁰(101-digit number)
16672321209656956974…70940541894268129279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.334 × 10¹⁰⁰(101-digit number)
33344642419313913948…41881083788536258559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.668 × 10¹⁰⁰(101-digit number)
66689284838627827896…83762167577072517119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.333 × 10¹⁰¹(102-digit number)
13337856967725565579…67524335154145034239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.667 × 10¹⁰¹(102-digit number)
26675713935451131158…35048670308290068479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.335 × 10¹⁰¹(102-digit number)
53351427870902262317…70097340616580136959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.067 × 10¹⁰²(103-digit number)
10670285574180452463…40194681233160273919
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:57,788,097 XPM·at block #6,818,003 · updates every 60s
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