Block #1,637,325

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/20/2016, 8:57:55 AM · Difficulty 10.6553 · 5,176,715 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e97ca957fc08a5edb0f00d01289f39aec6df184fa1f1325a457e8aa5240495a0

Height

#1,637,325

Difficulty

10.655274

Transactions

2

Size

43.05 KB

Version

2

Bits

0aa7c010

Nonce

250,337,843

Timestamp

6/20/2016, 8:57:55 AM

Confirmations

5,176,715

Merkle Root

b80aa5d400c22058970971ac5be8eb04baf3262bf4f3017218974acd89c0b214
Transactions (2)
1 in → 1 out9.6500 XPM109 B
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.

5.235 × 10⁹⁴(95-digit number)
52357962569537342140…65837489158358896641
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
5.235 × 10⁹⁴(95-digit number)
52357962569537342140…65837489158358896641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.047 × 10⁹⁵(96-digit number)
10471592513907468428…31674978316717793281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.094 × 10⁹⁵(96-digit number)
20943185027814936856…63349956633435586561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.188 × 10⁹⁵(96-digit number)
41886370055629873712…26699913266871173121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.377 × 10⁹⁵(96-digit number)
83772740111259747424…53399826533742346241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.675 × 10⁹⁶(97-digit number)
16754548022251949484…06799653067484692481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.350 × 10⁹⁶(97-digit number)
33509096044503898969…13599306134969384961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.701 × 10⁹⁶(97-digit number)
67018192089007797939…27198612269938769921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.340 × 10⁹⁷(98-digit number)
13403638417801559587…54397224539877539841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.680 × 10⁹⁷(98-digit number)
26807276835603119175…08794449079755079681
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:57,756,395 XPM·at block #6,814,039 · updates every 60s
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