Block #1,446,544

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/7/2016, 1:04:54 PM · Difficulty 10.7594 · 5,379,570 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e1ea8c4754ba834f6c8eacd55e067ffd36970f0b24ea4f77b9587205aea5a67a

Height

#1,446,544

Difficulty

10.759384

Transactions

2

Size

1.18 KB

Version

2

Bits

0ac266fa

Nonce

165,799,586

Timestamp

2/7/2016, 1:04:54 PM

Confirmations

5,379,570

Merkle Root

bc89aba55ec3dffde355b6e7f82743397c852b4e7cffc466bb546df7fd75a6d2
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.

1.933 × 10⁹⁴(95-digit number)
19337593564714166672…67508054466920527359
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
1.933 × 10⁹⁴(95-digit number)
19337593564714166672…67508054466920527359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.867 × 10⁹⁴(95-digit number)
38675187129428333344…35016108933841054719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.735 × 10⁹⁴(95-digit number)
77350374258856666689…70032217867682109439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.547 × 10⁹⁵(96-digit number)
15470074851771333337…40064435735364218879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.094 × 10⁹⁵(96-digit number)
30940149703542666675…80128871470728437759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.188 × 10⁹⁵(96-digit number)
61880299407085333351…60257742941456875519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.237 × 10⁹⁶(97-digit number)
12376059881417066670…20515485882913751039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.475 × 10⁹⁶(97-digit number)
24752119762834133340…41030971765827502079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.950 × 10⁹⁶(97-digit number)
49504239525668266681…82061943531655004159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.900 × 10⁹⁶(97-digit number)
99008479051336533362…64123887063310008319
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:57,853,037 XPM·at block #6,826,113 · updates every 60s
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