Block #492,517

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/15/2014, 4:58:01 AM · Difficulty 10.6875 · 6,303,555 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c47e911953dfa69adf20dabe5dc409fb28d661a689b215703dd30fcce343cdc2

Height

#492,517

Difficulty

10.687461

Transactions

2

Size

724 B

Version

2

Bits

0aaffd6d

Nonce

82,254

Timestamp

4/15/2014, 4:58:01 AM

Confirmations

6,303,555

Merkle Root

0fe32e5c2a108b164208d06bbdbb7c5450a43b336478ea9396b1eb9db754cd4b
Transactions (2)
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.

3.530 × 10¹⁰¹(102-digit number)
35300487936734527847…25674772401433214081
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
3.530 × 10¹⁰¹(102-digit number)
35300487936734527847…25674772401433214081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.060 × 10¹⁰¹(102-digit number)
70600975873469055694…51349544802866428161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.412 × 10¹⁰²(103-digit number)
14120195174693811138…02699089605732856321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.824 × 10¹⁰²(103-digit number)
28240390349387622277…05398179211465712641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.648 × 10¹⁰²(103-digit number)
56480780698775244555…10796358422931425281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.129 × 10¹⁰³(104-digit number)
11296156139755048911…21592716845862850561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.259 × 10¹⁰³(104-digit number)
22592312279510097822…43185433691725701121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.518 × 10¹⁰³(104-digit number)
45184624559020195644…86370867383451402241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.036 × 10¹⁰³(104-digit number)
90369249118040391288…72741734766902804481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.807 × 10¹⁰⁴(105-digit number)
18073849823608078257…45483469533805608961
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:57,612,672 XPM·at block #6,796,071 · updates every 60s
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