Block #1,495,334

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 3/13/2016, 7:05:38 PM · Difficulty 10.6466 · 5,344,793 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cee1bb31449f2b802e8a6eeb2693adce5879615bc702a6da4cb4bd0490d43494

Height

#1,495,334

Difficulty

10.646561

Transactions

2

Size

1.45 KB

Version

2

Bits

0aa58500

Nonce

1,273,306,671

Timestamp

3/13/2016, 7:05:38 PM

Confirmations

5,344,793

Merkle Root

45699c2332a62e47323253035195a8e4004b46080d36dc71b743d4b985210c2f
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.

1.471 × 10⁹⁵(96-digit number)
14710478705058035579…72277998285190502001
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
1.471 × 10⁹⁵(96-digit number)
14710478705058035579…72277998285190502001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.942 × 10⁹⁵(96-digit number)
29420957410116071158…44555996570381004001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.884 × 10⁹⁵(96-digit number)
58841914820232142317…89111993140762008001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.176 × 10⁹⁶(97-digit number)
11768382964046428463…78223986281524016001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.353 × 10⁹⁶(97-digit number)
23536765928092856927…56447972563048032001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.707 × 10⁹⁶(97-digit number)
47073531856185713854…12895945126096064001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.414 × 10⁹⁶(97-digit number)
94147063712371427708…25791890252192128001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.882 × 10⁹⁷(98-digit number)
18829412742474285541…51583780504384256001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.765 × 10⁹⁷(98-digit number)
37658825484948571083…03167561008768512001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.531 × 10⁹⁷(98-digit number)
75317650969897142166…06335122017537024001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.506 × 10⁹⁸(99-digit number)
15063530193979428433…12670244035074048001
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,965,330 XPM·at block #6,840,126 · updates every 60s
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