Block #1,567,242

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/1/2016, 10:05:17 AM · Difficulty 10.7592 · 5,258,942 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2bca2b5f22d81c37026cbdc91a6063345b5be2b951cafb92cc6a59edb379bcbc

Height

#1,567,242

Difficulty

10.759204

Transactions

2

Size

866 B

Version

2

Bits

0ac25b39

Nonce

1,858,389,529

Timestamp

5/1/2016, 10:05:17 AM

Confirmations

5,258,942

Merkle Root

849b77eaa925566bf43f4029f3105c2bba2d7f80a75b33f3329bbc9fe9a4ecfd
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.

6.988 × 10⁹⁴(95-digit number)
69883352716078889398…69365557775874524159
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
6.988 × 10⁹⁴(95-digit number)
69883352716078889398…69365557775874524159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.397 × 10⁹⁵(96-digit number)
13976670543215777879…38731115551749048319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.795 × 10⁹⁵(96-digit number)
27953341086431555759…77462231103498096639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.590 × 10⁹⁵(96-digit number)
55906682172863111518…54924462206996193279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.118 × 10⁹⁶(97-digit number)
11181336434572622303…09848924413992386559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.236 × 10⁹⁶(97-digit number)
22362672869145244607…19697848827984773119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.472 × 10⁹⁶(97-digit number)
44725345738290489215…39395697655969546239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.945 × 10⁹⁶(97-digit number)
89450691476580978430…78791395311939092479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.789 × 10⁹⁷(98-digit number)
17890138295316195686…57582790623878184959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.578 × 10⁹⁷(98-digit number)
35780276590632391372…15165581247756369919
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:57,853,601 XPM·at block #6,826,183 · updates every 60s
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