Block #383,108

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/31/2014, 5:13:07 AM · Difficulty 10.3976 · 6,409,700 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
479fd8ef12d9e4c56c9b2ae4455a190d64f65e4e4acad8e38be5f59525562905

Height

#383,108

Difficulty

10.397585

Transactions

3

Size

656 B

Version

2

Bits

0a65c821

Nonce

15,064

Timestamp

1/31/2014, 5:13:07 AM

Confirmations

6,409,700

Merkle Root

31bc33ecbf84ff106359c1ed405cbcc880ef90a127ed68bc797b8a935713761d
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.

1.492 × 10⁹⁹(100-digit number)
14928240266921743112…57799986449526138881
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
1.492 × 10⁹⁹(100-digit number)
14928240266921743112…57799986449526138881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.985 × 10⁹⁹(100-digit number)
29856480533843486225…15599972899052277761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.971 × 10⁹⁹(100-digit number)
59712961067686972450…31199945798104555521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.194 × 10¹⁰⁰(101-digit number)
11942592213537394490…62399891596209111041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.388 × 10¹⁰⁰(101-digit number)
23885184427074788980…24799783192418222081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.777 × 10¹⁰⁰(101-digit number)
47770368854149577960…49599566384836444161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.554 × 10¹⁰⁰(101-digit number)
95540737708299155920…99199132769672888321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.910 × 10¹⁰¹(102-digit number)
19108147541659831184…98398265539345776641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.821 × 10¹⁰¹(102-digit number)
38216295083319662368…96796531078691553281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.643 × 10¹⁰¹(102-digit number)
76432590166639324736…93593062157383106561
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:57,586,448 XPM·at block #6,792,807 · updates every 60s
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