Block #1,552,043

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/22/2016, 4:07:39 AM · Difficulty 10.6497 · 5,275,158 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
327964d84bb2e7631ed8f202065c8d82e346b5e3d2f9cc0a20db9aae246fd967

Height

#1,552,043

Difficulty

10.649727

Transactions

2

Size

832 B

Version

2

Bits

0aa6547a

Nonce

459,109,838

Timestamp

4/22/2016, 4:07:39 AM

Confirmations

5,275,158

Merkle Root

124573aebf69fecd683137010d393e8e285a399bf7f11fdd281d86be06e4a8e3
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.

2.048 × 10⁹³(94-digit number)
20484944623141668329…52270837951319086079
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
2.048 × 10⁹³(94-digit number)
20484944623141668329…52270837951319086079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.096 × 10⁹³(94-digit number)
40969889246283336658…04541675902638172159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.193 × 10⁹³(94-digit number)
81939778492566673316…09083351805276344319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.638 × 10⁹⁴(95-digit number)
16387955698513334663…18166703610552688639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.277 × 10⁹⁴(95-digit number)
32775911397026669326…36333407221105377279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.555 × 10⁹⁴(95-digit number)
65551822794053338653…72666814442210754559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.311 × 10⁹⁵(96-digit number)
13110364558810667730…45333628884421509119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.622 × 10⁹⁵(96-digit number)
26220729117621335461…90667257768843018239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.244 × 10⁹⁵(96-digit number)
52441458235242670922…81334515537686036479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.048 × 10⁹⁶(97-digit number)
10488291647048534184…62669031075372072959
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:57,861,705 XPM·at block #6,827,200 · updates every 60s
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