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Block #243,936

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/4/2013, 2:01:38 PM Β· Difficulty 9.9622 Β· 6,589,958 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ab8286b934e95893b54b9bcc62fe2519e2d8e57fe819476445ca50861365603f
View on Chainz β†—

Height

#243,936

Difficulty

9.962243

Transactions

2

Size

5.00 KB

Version

2

Bits

09f65592

Nonce

24,153

Timestamp

11/4/2013, 2:01:38 PM

Confirmations

6,589,958

Mined by

⛏️ P2SHAaXb6LdzMFohbBjmNyta5dnWNNXefG91jF

Merkle Root

6fb8e54e6a3ef73684fa5e5e04998f96bb0f4686d36b6c6716c018599b518867
Transactions (2)
Coinbasee66f206a03bb05…7e06de52bf18e0
1 in β†’ 1 out10.1100 XPM100 B
AaXb6Ldz…XefG91jF
d9b338a65d959d…12cdcf3bb2a93b
33 in β†’ 1 out4.2962 XPM4.81 KB
Acy5hWbh…uFhC2Yj9
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.

1.251 Γ— 10⁹⁢(97-digit number)
12515471099524511721…10465337719779561279
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
1.251 Γ— 10⁹⁢(97-digit number)
12515471099524511721…10465337719779561279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.503 Γ— 10⁹⁢(97-digit number)
25030942199049023443…20930675439559122559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.006 Γ— 10⁹⁢(97-digit number)
50061884398098046887…41861350879118245119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.001 Γ— 10⁹⁷(98-digit number)
10012376879619609377…83722701758236490239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.002 Γ— 10⁹⁷(98-digit number)
20024753759239218755…67445403516472980479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.004 Γ— 10⁹⁷(98-digit number)
40049507518478437510…34890807032945960959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.009 Γ— 10⁹⁷(98-digit number)
80099015036956875020…69781614065891921919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.601 Γ— 10⁹⁸(99-digit number)
16019803007391375004…39563228131783843839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.203 Γ— 10⁹⁸(99-digit number)
32039606014782750008…79126456263567687679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,915,376 XPMΒ·at block #6,833,893 Β· updates every 60s
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