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Block #2,466,001

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/10/2018, 2:36:18 AM Β· Difficulty 10.9603 Β· 4,377,098 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0943a70358ced589e6593024cd6f3bea43c539c78a63125c90e8578988f17230
View on Chainz β†—

Height

#2,466,001

Difficulty

10.960343

Transactions

2

Size

425 B

Version

2

Bits

0af5d909

Nonce

643,310,235

Timestamp

1/10/2018, 2:36:18 AM

Confirmations

4,377,098

Mined by

⛏️ P2SHAY73TfGgHs1LjSYAv5KgySUF9MrST9NVFC

Merkle Root

adfd5f0e07409a5379aeff8a0bc249fac3b57a0dfd4e2a9650f0a2ca7ef58873
Transactions (2)
Coinbaseb229be01fa14ab…686071540cfc32
1 in β†’ 1 out8.3200 XPM109 B
AY73TfGg…rST9NVFC
f3eb4523d78ee5…6cb4e4e4dce73d
1 in β†’ 2 out4741.7831 XPM227 B
AK5G1ZB2…bbh6gpXYAXwsmPPr…6VMrFrtM
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.

1.083 Γ— 10⁹³(94-digit number)
10830033251272595300…01735326706696687359
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
1.083 Γ— 10⁹³(94-digit number)
10830033251272595300…01735326706696687359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.166 Γ— 10⁹³(94-digit number)
21660066502545190600…03470653413393374719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.332 Γ— 10⁹³(94-digit number)
43320133005090381201…06941306826786749439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.664 Γ— 10⁹³(94-digit number)
86640266010180762402…13882613653573498879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.732 Γ— 10⁹⁴(95-digit number)
17328053202036152480…27765227307146997759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.465 Γ— 10⁹⁴(95-digit number)
34656106404072304960…55530454614293995519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.931 Γ— 10⁹⁴(95-digit number)
69312212808144609921…11060909228587991039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.386 Γ— 10⁹⁡(96-digit number)
13862442561628921984…22121818457175982079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.772 Γ— 10⁹⁡(96-digit number)
27724885123257843968…44243636914351964159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.544 Γ— 10⁹⁡(96-digit number)
55449770246515687937…88487273828703928319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.108 Γ— 10⁹⁢(97-digit number)
11089954049303137587…76974547657407856639
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:57,989,155 XPMΒ·at block #6,843,098 Β· updates every 60s
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