Block #277,923

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 6:47:16 PM · Difficulty 9.9676 · 6,518,450 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c306472bab4e22a9e4fcfbdfe548c4e55994e9664130c127eb19b0c5ab29cd59

Height

#277,923

Difficulty

9.967564

Transactions

1

Size

968 B

Version

2

Bits

09f7b247

Nonce

85,424

Timestamp

11/27/2013, 6:47:16 PM

Confirmations

6,518,450

Merkle Root

25085224664c32fc13775e7042320f71ce41755235c40c6bd68dc7ca3faf3faf
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.

2.475 × 10⁹²(93-digit number)
24752631748301865089…33867187588683655679
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
2.475 × 10⁹²(93-digit number)
24752631748301865089…33867187588683655679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.950 × 10⁹²(93-digit number)
49505263496603730178…67734375177367311359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.901 × 10⁹²(93-digit number)
99010526993207460356…35468750354734622719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.980 × 10⁹³(94-digit number)
19802105398641492071…70937500709469245439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.960 × 10⁹³(94-digit number)
39604210797282984142…41875001418938490879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.920 × 10⁹³(94-digit number)
79208421594565968285…83750002837876981759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.584 × 10⁹⁴(95-digit number)
15841684318913193657…67500005675753963519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.168 × 10⁹⁴(95-digit number)
31683368637826387314…35000011351507927039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.336 × 10⁹⁴(95-digit number)
63366737275652774628…70000022703015854079
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:57,614,979 XPM·at block #6,796,372 · updates every 60s
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