Block #215,596

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/18/2013, 4:50:08 AM · Difficulty 9.9255 · 6,583,424 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
310b028ee7c0e878eb12f2e5ac73bcfec9fdda198f9efdb68ccef81acf2bee01

Height

#215,596

Difficulty

9.925507

Transactions

1

Size

6.52 KB

Version

2

Bits

09ecee0c

Nonce

1,164,930,512

Timestamp

10/18/2013, 4:50:08 AM

Confirmations

6,583,424

Merkle Root

bbdee1aa4e712519a7c3fa23db7493b2f58c042b5700daf8f1fe5a3cb383daaf
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.

3.250 × 10⁹⁵(96-digit number)
32503133175207667783…14439756501582091279
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
3.250 × 10⁹⁵(96-digit number)
32503133175207667783…14439756501582091279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.500 × 10⁹⁵(96-digit number)
65006266350415335566…28879513003164182559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.300 × 10⁹⁶(97-digit number)
13001253270083067113…57759026006328365119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.600 × 10⁹⁶(97-digit number)
26002506540166134226…15518052012656730239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.200 × 10⁹⁶(97-digit number)
52005013080332268453…31036104025313460479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.040 × 10⁹⁷(98-digit number)
10401002616066453690…62072208050626920959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.080 × 10⁹⁷(98-digit number)
20802005232132907381…24144416101253841919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.160 × 10⁹⁷(98-digit number)
41604010464265814762…48288832202507683839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.320 × 10⁹⁷(98-digit number)
83208020928531629525…96577664405015367679
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:57,636,204 XPM·at block #6,799,019 · updates every 60s
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