Block #99,904

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/5/2013, 10:02:03 PM · Difficulty 9.4062 · 6,696,381 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2f01981f5d2fd85e88a8069f3b87aa534cc1d3a5c340f13da6f219410dbdb8c7

Height

#99,904

Difficulty

9.406201

Transactions

2

Size

358 B

Version

2

Bits

0967fcd0

Nonce

471,001

Timestamp

8/5/2013, 10:02:03 PM

Confirmations

6,696,381

Merkle Root

b8b940f630fc4461f964b78c4643f930188c179535016f3ca42a44a975501338
Transactions (2)
1 in → 1 out11.3000 XPM109 B
1 in → 1 out11.5900 XPM158 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.

1.758 × 10⁹⁶(97-digit number)
17588577173772852566…89553233709715727799
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
1.758 × 10⁹⁶(97-digit number)
17588577173772852566…89553233709715727799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.517 × 10⁹⁶(97-digit number)
35177154347545705133…79106467419431455599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.035 × 10⁹⁶(97-digit number)
70354308695091410267…58212934838862911199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.407 × 10⁹⁷(98-digit number)
14070861739018282053…16425869677725822399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.814 × 10⁹⁷(98-digit number)
28141723478036564106…32851739355451644799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.628 × 10⁹⁷(98-digit number)
56283446956073128213…65703478710903289599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.125 × 10⁹⁸(99-digit number)
11256689391214625642…31406957421806579199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.251 × 10⁹⁸(99-digit number)
22513378782429251285…62813914843613158399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.502 × 10⁹⁸(99-digit number)
45026757564858502571…25627829687226316799
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:57,614,283 XPM·at block #6,796,284 · updates every 60s
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