Block #1,935,652

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/12/2017, 8:38:15 AM · Difficulty 10.7646 · 4,906,992 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0dd40529b31bf117b07d1e20b48423ac87c18dbcde9ae3867ddb4623a4414c77

Height

#1,935,652

Difficulty

10.764623

Transactions

2

Size

70.91 KB

Version

2

Bits

0ac3be51

Nonce

101,784,138

Timestamp

1/12/2017, 8:38:15 AM

Confirmations

4,906,992

Merkle Root

1c1f66f6d28ea1aba161414992a51c98dc17628c8f66a40568f4847a9ed4922d
Transactions (2)
1 in → 1 out9.3500 XPM110 B
489 in → 1 out185080.3358 XPM70.71 KB
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.

1.203 × 10⁹⁶(97-digit number)
12033130831967403115…31326089221497989119
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
1.203 × 10⁹⁶(97-digit number)
12033130831967403115…31326089221497989119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.406 × 10⁹⁶(97-digit number)
24066261663934806230…62652178442995978239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.813 × 10⁹⁶(97-digit number)
48132523327869612460…25304356885991956479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.626 × 10⁹⁶(97-digit number)
96265046655739224920…50608713771983912959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.925 × 10⁹⁷(98-digit number)
19253009331147844984…01217427543967825919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.850 × 10⁹⁷(98-digit number)
38506018662295689968…02434855087935651839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.701 × 10⁹⁷(98-digit number)
77012037324591379936…04869710175871303679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.540 × 10⁹⁸(99-digit number)
15402407464918275987…09739420351742607359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.080 × 10⁹⁸(99-digit number)
30804814929836551974…19478840703485214719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.160 × 10⁹⁸(99-digit number)
61609629859673103948…38957681406970429439
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:57,985,586 XPM·at block #6,842,643 · updates every 60s
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