Block #144,197

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/1/2013, 4:09:52 AM · Difficulty 9.8381 · 6,650,012 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
90652a1f16bdfd0a1ae29b78ac7c680d681643f3b8231dacf6d0f9aea0f9bb3a

Height

#144,197

Difficulty

9.838149

Transactions

5

Size

1.22 KB

Version

2

Bits

09d690f1

Nonce

84,399

Timestamp

9/1/2013, 4:09:52 AM

Confirmations

6,650,012

Merkle Root

013038468aeb55a4ad23f0e9ca68481af84ea77e02b6ebb3402ea6bd1f6099e6
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.

1.336 × 10⁹⁵(96-digit number)
13368348300016631371…19328197274051355579
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
1.336 × 10⁹⁵(96-digit number)
13368348300016631371…19328197274051355579
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.673 × 10⁹⁵(96-digit number)
26736696600033262743…38656394548102711159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.347 × 10⁹⁵(96-digit number)
53473393200066525487…77312789096205422319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.069 × 10⁹⁶(97-digit number)
10694678640013305097…54625578192410844639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.138 × 10⁹⁶(97-digit number)
21389357280026610194…09251156384821689279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.277 × 10⁹⁶(97-digit number)
42778714560053220389…18502312769643378559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.555 × 10⁹⁶(97-digit number)
85557429120106440779…37004625539286757119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.711 × 10⁹⁷(98-digit number)
17111485824021288155…74009251078573514239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.422 × 10⁹⁷(98-digit number)
34222971648042576311…48018502157147028479
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:57,597,698 XPM·at block #6,794,208 · updates every 60s
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