Block #608,787

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/30/2014, 9:12:16 PM · Difficulty 10.9092 · 6,185,480 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7140e86246d0c1a4743b091bebe50fb140b59a37c31025d3aa124b661fb82632

Height

#608,787

Difficulty

10.909155

Transactions

4

Size

1.59 KB

Version

2

Bits

0ae8be61

Nonce

1,185,186,418

Timestamp

6/30/2014, 9:12:16 PM

Confirmations

6,185,480

Merkle Root

edd1ec6b153f6deac6b6a3eba95f1062065a397b8edf1cd730313ae7e22a951f
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.

1.355 × 10¹⁰⁰(101-digit number)
13558484963465186652…44472004505038003201
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
1.355 × 10¹⁰⁰(101-digit number)
13558484963465186652…44472004505038003201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.711 × 10¹⁰⁰(101-digit number)
27116969926930373304…88944009010076006401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.423 × 10¹⁰⁰(101-digit number)
54233939853860746609…77888018020152012801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.084 × 10¹⁰¹(102-digit number)
10846787970772149321…55776036040304025601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.169 × 10¹⁰¹(102-digit number)
21693575941544298643…11552072080608051201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.338 × 10¹⁰¹(102-digit number)
43387151883088597287…23104144161216102401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.677 × 10¹⁰¹(102-digit number)
86774303766177194575…46208288322432204801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.735 × 10¹⁰²(103-digit number)
17354860753235438915…92416576644864409601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.470 × 10¹⁰²(103-digit number)
34709721506470877830…84833153289728819201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.941 × 10¹⁰²(103-digit number)
69419443012941755660…69666306579457638401
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,598,164 XPM·at block #6,794,266 · updates every 60s
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