Block #152,087

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/6/2013, 2:22:30 AM · Difficulty 9.8622 · 6,654,173 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
899ff27410535a8b622af7f6e14b3fd7f55e8cba1a8e96eaf50347ef928af25a

Height

#152,087

Difficulty

9.862176

Transactions

1

Size

201 B

Version

2

Bits

09dcb78e

Nonce

66,213

Timestamp

9/6/2013, 2:22:30 AM

Confirmations

6,654,173

Merkle Root

efffdcc3a874c1428a62643c5ce0928f1e2ec0a9a1bfa011a1fade5c8b2ae0b6
Transactions (1)
1 in → 1 out10.2700 XPM109 B
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.

1.604 × 10⁹⁹(100-digit number)
16041092690592008512…00117747333795936799
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
1.604 × 10⁹⁹(100-digit number)
16041092690592008512…00117747333795936799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.208 × 10⁹⁹(100-digit number)
32082185381184017024…00235494667591873599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.416 × 10⁹⁹(100-digit number)
64164370762368034049…00470989335183747199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.283 × 10¹⁰⁰(101-digit number)
12832874152473606809…00941978670367494399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.566 × 10¹⁰⁰(101-digit number)
25665748304947213619…01883957340734988799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.133 × 10¹⁰⁰(101-digit number)
51331496609894427239…03767914681469977599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.026 × 10¹⁰¹(102-digit number)
10266299321978885447…07535829362939955199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.053 × 10¹⁰¹(102-digit number)
20532598643957770895…15071658725879910399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.106 × 10¹⁰¹(102-digit number)
41065197287915541791…30143317451759820799
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,694,164 XPM·at block #6,806,259 · updates every 60s
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