Block #276,063

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 12:14:18 AM · Difficulty 9.9623 · 6,519,776 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5d863d50e05825d900fafa02eee73ca97828f93842fa5cebaba15a3766b1f9f1

Height

#276,063

Difficulty

9.962305

Transactions

1

Size

970 B

Version

2

Bits

09f65998

Nonce

40,392

Timestamp

11/27/2013, 12:14:18 AM

Confirmations

6,519,776

Merkle Root

96a35f3e408f4714661215154e6d8862612a612aac41b63bdbcf2c913a55d382
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.

2.286 × 10⁹⁷(98-digit number)
22865048690254225269…55632581301325736959
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
2.286 × 10⁹⁷(98-digit number)
22865048690254225269…55632581301325736959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.573 × 10⁹⁷(98-digit number)
45730097380508450539…11265162602651473919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.146 × 10⁹⁷(98-digit number)
91460194761016901079…22530325205302947839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.829 × 10⁹⁸(99-digit number)
18292038952203380215…45060650410605895679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.658 × 10⁹⁸(99-digit number)
36584077904406760431…90121300821211791359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.316 × 10⁹⁸(99-digit number)
73168155808813520863…80242601642423582719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.463 × 10⁹⁹(100-digit number)
14633631161762704172…60485203284847165439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.926 × 10⁹⁹(100-digit number)
29267262323525408345…20970406569694330879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.853 × 10⁹⁹(100-digit number)
58534524647050816690…41940813139388661759
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,610,795 XPM·at block #6,795,838 · updates every 60s
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