Block #377,715

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2014, 8:12:20 AM · Difficulty 10.4182 · 6,432,521 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
305e2abd2fe71d6431f721e8f88297bc3001e51fa7344c69907d63c6ef8320cd

Height

#377,715

Difficulty

10.418204

Transactions

2

Size

584 B

Version

2

Bits

0a6b0f71

Nonce

170,081

Timestamp

1/27/2014, 8:12:20 AM

Confirmations

6,432,521

Merkle Root

00a97a24f8284edf0f3e499f140af9cf183359842e3a94720a6c3f7f38e04632
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.

1.954 × 10¹⁰¹(102-digit number)
19547562597562143753…30478969344456028161
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
1.954 × 10¹⁰¹(102-digit number)
19547562597562143753…30478969344456028161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.909 × 10¹⁰¹(102-digit number)
39095125195124287506…60957938688912056321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.819 × 10¹⁰¹(102-digit number)
78190250390248575013…21915877377824112641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.563 × 10¹⁰²(103-digit number)
15638050078049715002…43831754755648225281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.127 × 10¹⁰²(103-digit number)
31276100156099430005…87663509511296450561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.255 × 10¹⁰²(103-digit number)
62552200312198860011…75327019022592901121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.251 × 10¹⁰³(104-digit number)
12510440062439772002…50654038045185802241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.502 × 10¹⁰³(104-digit number)
25020880124879544004…01308076090371604481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.004 × 10¹⁰³(104-digit number)
50041760249759088008…02616152180743208961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.000 × 10¹⁰⁴(105-digit number)
10008352049951817601…05232304361486417921
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:57,725,965 XPM·at block #6,810,235 · updates every 60s
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