Block #1,425,703

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/23/2016, 11:06:11 PM · Difficulty 10.7660 · 5,413,342 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
33723d870532a9cf7167dd27fb2aa2751662e8df740180d60abb7d7c355ecc38

Height

#1,425,703

Difficulty

10.765971

Transactions

2

Size

834 B

Version

2

Bits

0ac416b1

Nonce

513,014,754

Timestamp

1/23/2016, 11:06:11 PM

Confirmations

5,413,342

Merkle Root

94641a9bd943eadedf11e4d8ef871a0c32eff8e67c1eb48195f3e42c433a2255
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.

1.692 × 10⁹⁶(97-digit number)
16929493557560408479…72684415348947148799
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
1.692 × 10⁹⁶(97-digit number)
16929493557560408479…72684415348947148799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.385 × 10⁹⁶(97-digit number)
33858987115120816958…45368830697894297599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.771 × 10⁹⁶(97-digit number)
67717974230241633916…90737661395788595199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.354 × 10⁹⁷(98-digit number)
13543594846048326783…81475322791577190399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.708 × 10⁹⁷(98-digit number)
27087189692096653566…62950645583154380799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.417 × 10⁹⁷(98-digit number)
54174379384193307133…25901291166308761599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.083 × 10⁹⁸(99-digit number)
10834875876838661426…51802582332617523199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.166 × 10⁹⁸(99-digit number)
21669751753677322853…03605164665235046399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.333 × 10⁹⁸(99-digit number)
43339503507354645706…07210329330470092799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.667 × 10⁹⁸(99-digit number)
86679007014709291413…14420658660940185599
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,956,629 XPM·at block #6,839,044 · updates every 60s
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