Block #255,064

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/11/2013, 1:58:03 AM · Difficulty 9.9738 · 6,536,900 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
984d4e4762ede91230d828667b24860556bb16bb435a920d6ae136a3b1633654

Height

#255,064

Difficulty

9.973773

Transactions

4

Size

1.60 KB

Version

2

Bits

09f94935

Nonce

4,209

Timestamp

11/11/2013, 1:58:03 AM

Confirmations

6,536,900

Merkle Root

7aa3b4e9c755feb8d8cca4fba2cbdfa12482be21ebd2158d74a6a3133ec99a75
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.

9.954 × 10⁹⁴(95-digit number)
99544876547534029012…78770039786088817479
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
9.954 × 10⁹⁴(95-digit number)
99544876547534029012…78770039786088817479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.990 × 10⁹⁵(96-digit number)
19908975309506805802…57540079572177634959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.981 × 10⁹⁵(96-digit number)
39817950619013611604…15080159144355269919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.963 × 10⁹⁵(96-digit number)
79635901238027223209…30160318288710539839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.592 × 10⁹⁶(97-digit number)
15927180247605444641…60320636577421079679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.185 × 10⁹⁶(97-digit number)
31854360495210889283…20641273154842159359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.370 × 10⁹⁶(97-digit number)
63708720990421778567…41282546309684318719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.274 × 10⁹⁷(98-digit number)
12741744198084355713…82565092619368637439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.548 × 10⁹⁷(98-digit number)
25483488396168711427…65130185238737274879
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:57,579,669 XPM·at block #6,791,963 · updates every 60s
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