Block #1,560,350

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/27/2016, 4:55:49 AM · Difficulty 10.7163 · 5,266,724 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e4c69ee489962e7da82e2d6fc00b516321faf64dd339ff5c8ef743bd34f50066

Height

#1,560,350

Difficulty

10.716343

Transactions

2

Size

1015 B

Version

2

Bits

0ab7623d

Nonce

1,201,703,515

Timestamp

4/27/2016, 4:55:49 AM

Confirmations

5,266,724

Merkle Root

b40af33064e590e2f1d6104a9963a56ccceaf4c965e20d1996f3bd6cc96ab392
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.

3.588 × 10⁹²(93-digit number)
35886795203248266201…05417797494335036199
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
3.588 × 10⁹²(93-digit number)
35886795203248266201…05417797494335036199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.177 × 10⁹²(93-digit number)
71773590406496532403…10835594988670072399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.435 × 10⁹³(94-digit number)
14354718081299306480…21671189977340144799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.870 × 10⁹³(94-digit number)
28709436162598612961…43342379954680289599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.741 × 10⁹³(94-digit number)
57418872325197225922…86684759909360579199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.148 × 10⁹⁴(95-digit number)
11483774465039445184…73369519818721158399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.296 × 10⁹⁴(95-digit number)
22967548930078890369…46739039637442316799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.593 × 10⁹⁴(95-digit number)
45935097860157780738…93478079274884633599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.187 × 10⁹⁴(95-digit number)
91870195720315561476…86956158549769267199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.837 × 10⁹⁵(96-digit number)
18374039144063112295…73912317099538534399
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:57,860,775 XPM·at block #6,827,073 · updates every 60s
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