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Block #2,642,149

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2018, 3:06:17 PM Β· Difficulty 11.6439 Β· 4,196,128 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
84051213d0b9663b76d153a04ce19ba5d6b3b52d461101d65e1dfa8d0fe6ea8e
View on Chainz β†—

Height

#2,642,149

Difficulty

11.643926

Transactions

3

Size

618 B

Version

2

Bits

0ba4d853

Nonce

176,045,707

Timestamp

5/1/2018, 3:06:17 PM

Confirmations

4,196,128

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

41b15315dfa0910eea5113474c470ee51f20b844ce305b7bfadf10f7a556f83d
Transactions (3)
Coinbaseacb47aa0800b38…3c46f6482a6b07
1 in β†’ 1 out7.3800 XPM110 B
Adqah8zh…1WwoHJ9t
2c23c15967391a…515d8a6f8255cd
1 in β†’ 1 out249.9900 XPM191 B
ASKGxD31…U3aAKe34
185b90892285d8…6216bd041c827f
1 in β†’ 2 out3499.9800 XPM227 B
AKWHzRrq…Gztyhr4pASz4Qb3U…N5uDYup9
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.

2.330 Γ— 10⁹³(94-digit number)
23303332411170021423…57238517328406679039
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
2.330 Γ— 10⁹³(94-digit number)
23303332411170021423…57238517328406679039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.660 Γ— 10⁹³(94-digit number)
46606664822340042846…14477034656813358079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.321 Γ— 10⁹³(94-digit number)
93213329644680085693…28954069313626716159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.864 Γ— 10⁹⁴(95-digit number)
18642665928936017138…57908138627253432319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.728 Γ— 10⁹⁴(95-digit number)
37285331857872034277…15816277254506864639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.457 Γ— 10⁹⁴(95-digit number)
74570663715744068554…31632554509013729279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.491 Γ— 10⁹⁡(96-digit number)
14914132743148813710…63265109018027458559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.982 Γ— 10⁹⁡(96-digit number)
29828265486297627421…26530218036054917119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.965 Γ— 10⁹⁡(96-digit number)
59656530972595254843…53060436072109834239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.193 Γ— 10⁹⁢(97-digit number)
11931306194519050968…06120872144219668479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.386 Γ— 10⁹⁢(97-digit number)
23862612389038101937…12241744288439336959
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:57,950,496 XPMΒ·at block #6,838,276 Β· updates every 60s
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