Block #915,101

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/29/2015, 9:38:57 PM · Difficulty 10.9262 · 5,890,931 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3b2bb7fa4f8d3174e48a2de5fd086e5b0d74ae114c546cc2e4160595e155a60a

Height

#915,101

Difficulty

10.926205

Transactions

5

Size

1.20 KB

Version

2

Bits

0aed1bc2

Nonce

888,282,534

Timestamp

1/29/2015, 9:38:57 PM

Confirmations

5,890,931

Merkle Root

3183cafb12fa9d7eea2555626a7a64bce343fe3b0ed0311f3132d3e54c41f791
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.

3.063 × 10⁹⁷(98-digit number)
30635181098872650600…66646333457747676161
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
3.063 × 10⁹⁷(98-digit number)
30635181098872650600…66646333457747676161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.127 × 10⁹⁷(98-digit number)
61270362197745301200…33292666915495352321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.225 × 10⁹⁸(99-digit number)
12254072439549060240…66585333830990704641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.450 × 10⁹⁸(99-digit number)
24508144879098120480…33170667661981409281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.901 × 10⁹⁸(99-digit number)
49016289758196240960…66341335323962818561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.803 × 10⁹⁸(99-digit number)
98032579516392481920…32682670647925637121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.960 × 10⁹⁹(100-digit number)
19606515903278496384…65365341295851274241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.921 × 10⁹⁹(100-digit number)
39213031806556992768…30730682591702548481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.842 × 10⁹⁹(100-digit number)
78426063613113985536…61461365183405096961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.568 × 10¹⁰⁰(101-digit number)
15685212722622797107…22922730366810193921
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:57,692,335 XPM·at block #6,806,031 · updates every 60s
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