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Block #2,086,432

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/25/2017, 12:03:25 AM Β· Difficulty 10.8737 Β· 4,745,596 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cb43e6edd41fee7af14253d3a94ebf0b4f49b5f31f341e9d784bedbf3c846f53
View on Chainz β†—

Height

#2,086,432

Difficulty

10.873711

Transactions

2

Size

981 B

Version

2

Bits

0adfab7e

Nonce

253,930,310

Timestamp

4/25/2017, 12:03:25 AM

Confirmations

4,745,596

Mined by

⛏️ P2SHAX368Xmw2x7E73P4LsiABHRKM8i34x5QfY

Merkle Root

62f54e27d5e465d8338dcd6cda3762b8f18e24cc9eed031fea6744b6ce72ea72
Transactions (2)
Coinbasef8241e14250523…30b8ea178106d8
1 in β†’ 1 out8.4500 XPM109 B
AX368Xmw…i34x5QfY
dfd01d7bb0e33b…58e743b8b1b9be
5 in β†’ 1 out1824.1000 XPM782 B
AKc8GdcV…PFmVnxov
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.766 Γ— 10⁹⁡(96-digit number)
37668113332585256855…19313905879724669439
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.766 Γ— 10⁹⁡(96-digit number)
37668113332585256855…19313905879724669439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.533 Γ— 10⁹⁡(96-digit number)
75336226665170513710…38627811759449338879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.506 Γ— 10⁹⁢(97-digit number)
15067245333034102742…77255623518898677759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.013 Γ— 10⁹⁢(97-digit number)
30134490666068205484…54511247037797355519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.026 Γ— 10⁹⁢(97-digit number)
60268981332136410968…09022494075594711039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.205 Γ— 10⁹⁷(98-digit number)
12053796266427282193…18044988151189422079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.410 Γ— 10⁹⁷(98-digit number)
24107592532854564387…36089976302378844159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.821 Γ— 10⁹⁷(98-digit number)
48215185065709128774…72179952604757688319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.643 Γ— 10⁹⁷(98-digit number)
96430370131418257549…44359905209515376639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.928 Γ— 10⁹⁸(99-digit number)
19286074026283651509…88719810419030753279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.857 Γ— 10⁹⁸(99-digit number)
38572148052567303019…77439620838061506559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,900,355 XPMΒ·at block #6,832,027 Β· updates every 60s
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