Block #2,272,060

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/28/2017, 4:00:29 PM · Difficulty 10.9540 · 4,569,649 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9ac12ea8c9f11b26865a28bf0723c0771739102d5826a5455fefc5e08106d17d

Height

#2,272,060

Difficulty

10.953979

Transactions

6

Size

1.36 KB

Version

2

Bits

0af437ff

Nonce

51,476,983

Timestamp

8/28/2017, 4:00:29 PM

Confirmations

4,569,649

Merkle Root

205d89cf007033c560b4319b2894311d0605f3fb2fdf8905cd18656e1994c01a
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.

9.834 × 10⁹³(94-digit number)
98347380430028341896…62658825922780488241
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
9.834 × 10⁹³(94-digit number)
98347380430028341896…62658825922780488241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.966 × 10⁹⁴(95-digit number)
19669476086005668379…25317651845560976481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.933 × 10⁹⁴(95-digit number)
39338952172011336758…50635303691121952961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.867 × 10⁹⁴(95-digit number)
78677904344022673517…01270607382243905921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.573 × 10⁹⁵(96-digit number)
15735580868804534703…02541214764487811841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.147 × 10⁹⁵(96-digit number)
31471161737609069406…05082429528975623681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.294 × 10⁹⁵(96-digit number)
62942323475218138813…10164859057951247361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.258 × 10⁹⁶(97-digit number)
12588464695043627762…20329718115902494721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.517 × 10⁹⁶(97-digit number)
25176929390087255525…40659436231804989441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.035 × 10⁹⁶(97-digit number)
50353858780174511050…81318872463609978881
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,978,051 XPM·at block #6,841,708 · updates every 60s
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