Block #917,387

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/31/2015, 2:45:55 PM · Difficulty 10.9236 · 5,889,175 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
26ee949bee5f8221fcebd93c9de017b43577ddf781b79f199f03c8ebd62ada34

Height

#917,387

Difficulty

10.923598

Transactions

2

Size

579 B

Version

2

Bits

0aec70f1

Nonce

2,669,884,568

Timestamp

1/31/2015, 2:45:55 PM

Confirmations

5,889,175

Merkle Root

d6491ba48726c7b0f5b11c3188dc2315fe795d98c84673f238cbcfd3fcd8b0d8
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.

2.109 × 10⁹⁵(96-digit number)
21094086628780486890…77938051662131096839
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
2.109 × 10⁹⁵(96-digit number)
21094086628780486890…77938051662131096839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.218 × 10⁹⁵(96-digit number)
42188173257560973780…55876103324262193679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.437 × 10⁹⁵(96-digit number)
84376346515121947560…11752206648524387359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.687 × 10⁹⁶(97-digit number)
16875269303024389512…23504413297048774719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.375 × 10⁹⁶(97-digit number)
33750538606048779024…47008826594097549439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.750 × 10⁹⁶(97-digit number)
67501077212097558048…94017653188195098879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.350 × 10⁹⁷(98-digit number)
13500215442419511609…88035306376390197759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.700 × 10⁹⁷(98-digit number)
27000430884839023219…76070612752780395519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.400 × 10⁹⁷(98-digit number)
54000861769678046438…52141225505560791039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.080 × 10⁹⁸(99-digit number)
10800172353935609287…04282451011121582079
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:57,696,592 XPM·at block #6,806,561 · updates every 60s
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