Block #938,331

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/16/2015, 2:35:19 AM · Difficulty 10.9008 · 5,871,805 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1d4f01ccaeea8c1d8e15c7211b7c8d5e70b8eeb001a1e9ee41da64bd324ef950

Height

#938,331

Difficulty

10.900814

Transactions

5

Size

2.96 KB

Version

2

Bits

0ae69bba

Nonce

456,522,534

Timestamp

2/16/2015, 2:35:19 AM

Confirmations

5,871,805

Merkle Root

a2aa0855b2e9df85516c1d4b6c6d192fb14aa619a0cbaeb93e94b6b5cf73a08a
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.

6.415 × 10⁹⁶(97-digit number)
64152681475710991958…08145114259411189761
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
6.415 × 10⁹⁶(97-digit number)
64152681475710991958…08145114259411189761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.283 × 10⁹⁷(98-digit number)
12830536295142198391…16290228518822379521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.566 × 10⁹⁷(98-digit number)
25661072590284396783…32580457037644759041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.132 × 10⁹⁷(98-digit number)
51322145180568793566…65160914075289518081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.026 × 10⁹⁸(99-digit number)
10264429036113758713…30321828150579036161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.052 × 10⁹⁸(99-digit number)
20528858072227517426…60643656301158072321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.105 × 10⁹⁸(99-digit number)
41057716144455034853…21287312602316144641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.211 × 10⁹⁸(99-digit number)
82115432288910069707…42574625204632289281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.642 × 10⁹⁹(100-digit number)
16423086457782013941…85149250409264578561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.284 × 10⁹⁹(100-digit number)
32846172915564027882…70298500818529157121
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:57,725,155 XPM·at block #6,810,135 · updates every 60s
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