Block #1,095,044

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/8/2015, 7:30:19 AM · Difficulty 10.7476 · 5,721,141 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f531d0d45f7b5e86e34448a809749a4621599d3e2edeff55411e43b1c4751d5d

Height

#1,095,044

Difficulty

10.747647

Transactions

8

Size

5.57 KB

Version

2

Bits

0abf65d3

Nonce

210,414,771

Timestamp

6/8/2015, 7:30:19 AM

Confirmations

5,721,141

Merkle Root

acd443701d9985cba954e98d05e8117a96f7ad9a598b6ffb3a3de809ca889060
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.

1.442 × 10⁹⁴(95-digit number)
14425921223379030650…57633958610021505239
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
1.442 × 10⁹⁴(95-digit number)
14425921223379030650…57633958610021505239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.885 × 10⁹⁴(95-digit number)
28851842446758061300…15267917220043010479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.770 × 10⁹⁴(95-digit number)
57703684893516122600…30535834440086020959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.154 × 10⁹⁵(96-digit number)
11540736978703224520…61071668880172041919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.308 × 10⁹⁵(96-digit number)
23081473957406449040…22143337760344083839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.616 × 10⁹⁵(96-digit number)
46162947914812898080…44286675520688167679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.232 × 10⁹⁵(96-digit number)
92325895829625796160…88573351041376335359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.846 × 10⁹⁶(97-digit number)
18465179165925159232…77146702082752670719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.693 × 10⁹⁶(97-digit number)
36930358331850318464…54293404165505341439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.386 × 10⁹⁶(97-digit number)
73860716663700636928…08586808331010682879
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,773,606 XPM·at block #6,816,184 · updates every 60s
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