Block #1,493,413

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/12/2016, 6:04:38 AM · Difficulty 10.6669 · 5,333,548 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
42bc1166cf3bd050dd305790ecc091468f87b8264e98d61ae5884a5d20f96368

Height

#1,493,413

Difficulty

10.666884

Transactions

2

Size

1004 B

Version

2

Bits

0aaab8ec

Nonce

560,089,836

Timestamp

3/12/2016, 6:04:38 AM

Confirmations

5,333,548

Merkle Root

d5c9f1b77e5e7fb547be57966841fea9ba63bd0b3844ce993d135d2b9cb46bf0
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.

3.167 × 10⁹⁴(95-digit number)
31675504743212939336…30613888136454459119
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
3.167 × 10⁹⁴(95-digit number)
31675504743212939336…30613888136454459119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.335 × 10⁹⁴(95-digit number)
63351009486425878672…61227776272908918239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.267 × 10⁹⁵(96-digit number)
12670201897285175734…22455552545817836479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.534 × 10⁹⁵(96-digit number)
25340403794570351469…44911105091635672959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.068 × 10⁹⁵(96-digit number)
50680807589140702938…89822210183271345919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.013 × 10⁹⁶(97-digit number)
10136161517828140587…79644420366542691839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.027 × 10⁹⁶(97-digit number)
20272323035656281175…59288840733085383679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.054 × 10⁹⁶(97-digit number)
40544646071312562350…18577681466170767359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.108 × 10⁹⁶(97-digit number)
81089292142625124700…37155362932341534719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.621 × 10⁹⁷(98-digit number)
16217858428525024940…74310725864683069439
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:57,859,864 XPM·at block #6,826,960 · updates every 60s
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