Block #229,619

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/27/2013, 7:27:13 AM · Difficulty 9.9384 · 6,577,290 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
96c62a59b499e8428375e7a0a611ce37d5c74e61678c81d72eada489bdd91197

Height

#229,619

Difficulty

9.938431

Transactions

5

Size

1.22 KB

Version

2

Bits

09f03d0b

Nonce

62,896

Timestamp

10/27/2013, 7:27:13 AM

Confirmations

6,577,290

Merkle Root

27ac5789739710e3e0373783f8dc41d145fc3c86e6222fc4cfd56b75c5cdc552
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.

1.183 × 10⁹⁵(96-digit number)
11839577663586596472…38389862779805663999
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
1.183 × 10⁹⁵(96-digit number)
11839577663586596472…38389862779805663999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.367 × 10⁹⁵(96-digit number)
23679155327173192945…76779725559611327999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.735 × 10⁹⁵(96-digit number)
47358310654346385890…53559451119222655999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.471 × 10⁹⁵(96-digit number)
94716621308692771781…07118902238445311999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.894 × 10⁹⁶(97-digit number)
18943324261738554356…14237804476890623999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.788 × 10⁹⁶(97-digit number)
37886648523477108712…28475608953781247999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.577 × 10⁹⁶(97-digit number)
75773297046954217425…56951217907562495999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.515 × 10⁹⁷(98-digit number)
15154659409390843485…13902435815124991999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.030 × 10⁹⁷(98-digit number)
30309318818781686970…27804871630249983999
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:57,699,375 XPM·at block #6,806,908 · updates every 60s
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