Block #1,456,770

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/14/2016, 7:04:36 PM · Difficulty 10.7493 · 5,369,990 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b7e6c97d7dfbc22d0a09edec0971ecdff59cdb99b1bde470656d0f8b957b8106

Height

#1,456,770

Difficulty

10.749340

Transactions

2

Size

969 B

Version

2

Bits

0abfd4b7

Nonce

99,017,316

Timestamp

2/14/2016, 7:04:36 PM

Confirmations

5,369,990

Merkle Root

9bfc8eee7c0a3ad9ecacaf87cf675b93ca17243628b87109811fa1ed6c4f9618
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.

1.121 × 10⁹⁵(96-digit number)
11216295150244842136…66416010616824292479
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
1.121 × 10⁹⁵(96-digit number)
11216295150244842136…66416010616824292479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.243 × 10⁹⁵(96-digit number)
22432590300489684273…32832021233648584959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.486 × 10⁹⁵(96-digit number)
44865180600979368547…65664042467297169919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.973 × 10⁹⁵(96-digit number)
89730361201958737094…31328084934594339839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.794 × 10⁹⁶(97-digit number)
17946072240391747418…62656169869188679679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.589 × 10⁹⁶(97-digit number)
35892144480783494837…25312339738377359359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.178 × 10⁹⁶(97-digit number)
71784288961566989675…50624679476754718719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.435 × 10⁹⁷(98-digit number)
14356857792313397935…01249358953509437439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.871 × 10⁹⁷(98-digit number)
28713715584626795870…02498717907018874879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.742 × 10⁹⁷(98-digit number)
57427431169253591740…04997435814037749759
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:57,858,239 XPM·at block #6,826,759 · updates every 60s
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