Block #1,212,206

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/28/2015, 6:34:33 PM · Difficulty 10.7511 · 5,597,037 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c12ff64fd85024c8bbd45bfb88e3c3511674675401461cec219374fb79ae70fe

Height

#1,212,206

Difficulty

10.751113

Transactions

4

Size

5.74 KB

Version

2

Bits

0ac048f1

Nonce

84,782,825

Timestamp

8/28/2015, 6:34:33 PM

Confirmations

5,597,037

Merkle Root

f0a339372c69b089ac295cb5be7eba9203201cf0b3be3e6c65a25fed0bca2a13
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.

6.340 × 10⁹⁴(95-digit number)
63408818521424883120…24421168761096560639
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
6.340 × 10⁹⁴(95-digit number)
63408818521424883120…24421168761096560639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.268 × 10⁹⁵(96-digit number)
12681763704284976624…48842337522193121279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.536 × 10⁹⁵(96-digit number)
25363527408569953248…97684675044386242559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.072 × 10⁹⁵(96-digit number)
50727054817139906496…95369350088772485119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.014 × 10⁹⁶(97-digit number)
10145410963427981299…90738700177544970239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.029 × 10⁹⁶(97-digit number)
20290821926855962598…81477400355089940479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.058 × 10⁹⁶(97-digit number)
40581643853711925197…62954800710179880959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.116 × 10⁹⁶(97-digit number)
81163287707423850394…25909601420359761919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.623 × 10⁹⁷(98-digit number)
16232657541484770078…51819202840719523839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.246 × 10⁹⁷(98-digit number)
32465315082969540157…03638405681439047679
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,718,009 XPM·at block #6,809,242 · updates every 60s
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