Block #2,260,456

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/20/2017, 5:51:44 PM · Difficulty 10.9518 · 4,573,338 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a28d0fea6dc58830da2dfeb190f1bf713a0aff57607b389f50f368216acd9566

Height

#2,260,456

Difficulty

10.951810

Transactions

2

Size

426 B

Version

2

Bits

0af3a9ca

Nonce

253,199,532

Timestamp

8/20/2017, 5:51:44 PM

Confirmations

4,573,338

Merkle Root

a366b4630601c7d944fd239e45fa78d8a637aeb6347b75497457e3077c8babf0
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.

3.598 × 10⁹⁴(95-digit number)
35980814623265064671…22702880350270424361
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
3.598 × 10⁹⁴(95-digit number)
35980814623265064671…22702880350270424361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.196 × 10⁹⁴(95-digit number)
71961629246530129342…45405760700540848721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.439 × 10⁹⁵(96-digit number)
14392325849306025868…90811521401081697441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.878 × 10⁹⁵(96-digit number)
28784651698612051737…81623042802163394881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.756 × 10⁹⁵(96-digit number)
57569303397224103474…63246085604326789761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.151 × 10⁹⁶(97-digit number)
11513860679444820694…26492171208653579521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.302 × 10⁹⁶(97-digit number)
23027721358889641389…52984342417307159041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.605 × 10⁹⁶(97-digit number)
46055442717779282779…05968684834614318081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.211 × 10⁹⁶(97-digit number)
92110885435558565558…11937369669228636161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.842 × 10⁹⁷(98-digit number)
18422177087111713111…23874739338457272321
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:57,914,573 XPM·at block #6,833,793 · updates every 60s
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