Block #1,537,201

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/12/2016, 1:04:01 AM · Difficulty 10.6307 · 5,305,404 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
612e494ba08b4214ed27ad424fb2c9dc478ade564a7318c4b70dd21b67a07987

Height

#1,537,201

Difficulty

10.630729

Transactions

2

Size

630 B

Version

2

Bits

0aa17778

Nonce

2,090,514,442

Timestamp

4/12/2016, 1:04:01 AM

Confirmations

5,305,404

Merkle Root

2c8a706b585c376ad89d43c907752ed53ff745d4350829946649152d57e8b76f
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.

9.111 × 10⁹⁴(95-digit number)
91113870179949652904…59601949820862132479
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
9.111 × 10⁹⁴(95-digit number)
91113870179949652904…59601949820862132479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.822 × 10⁹⁵(96-digit number)
18222774035989930580…19203899641724264959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.644 × 10⁹⁵(96-digit number)
36445548071979861161…38407799283448529919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.289 × 10⁹⁵(96-digit number)
72891096143959722323…76815598566897059839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.457 × 10⁹⁶(97-digit number)
14578219228791944464…53631197133794119679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.915 × 10⁹⁶(97-digit number)
29156438457583888929…07262394267588239359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.831 × 10⁹⁶(97-digit number)
58312876915167777858…14524788535176478719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.166 × 10⁹⁷(98-digit number)
11662575383033555571…29049577070352957439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.332 × 10⁹⁷(98-digit number)
23325150766067111143…58099154140705914879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.665 × 10⁹⁷(98-digit number)
46650301532134222287…16198308281411829759
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:57,985,269 XPM·at block #6,842,604 · updates every 60s
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