Block #93,372

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/2/2013, 9:29:05 AM · Difficulty 9.1953 · 6,696,411 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8753d15a95e8d2ec467d6d400b6ccda647fd8283e21e0afd80ecefe55667e02a

Height

#93,372

Difficulty

9.195306

Transactions

2

Size

60.53 KB

Version

2

Bits

0931ff90

Nonce

20,261

Timestamp

8/2/2013, 9:29:05 AM

Confirmations

6,696,411

Merkle Root

3ec537f68e50e71af07dcedc57c21b84076e02b21d2a5d8c5591bf6c0d799371
Transactions (2)
1 in → 1 out12.4400 XPM109 B
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.

9.490 × 10¹¹⁴(115-digit number)
94903709298666557157…46519273498246012499
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
9.490 × 10¹¹⁴(115-digit number)
94903709298666557157…46519273498246012499
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.898 × 10¹¹⁵(116-digit number)
18980741859733311431…93038546996492024999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.796 × 10¹¹⁵(116-digit number)
37961483719466622863…86077093992984049999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.592 × 10¹¹⁵(116-digit number)
75922967438933245726…72154187985968099999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.518 × 10¹¹⁶(117-digit number)
15184593487786649145…44308375971936199999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.036 × 10¹¹⁶(117-digit number)
30369186975573298290…88616751943872399999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.073 × 10¹¹⁶(117-digit number)
60738373951146596581…77233503887744799999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.214 × 10¹¹⁷(118-digit number)
12147674790229319316…54467007775489599999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.429 × 10¹¹⁷(118-digit number)
24295349580458638632…08934015550979199999
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,562,234 XPM·at block #6,789,782 · updates every 60s