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Block #2,594,456

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/31/2018, 8:41:22 PM Β· Difficulty 11.3007 Β· 4,232,860 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
094eb2e28aaba912470fe97aa15360fb48c41c1fec4d04fda87499512dfeb0e4
View on Chainz β†—

Height

#2,594,456

Difficulty

11.300730

Transactions

2

Size

1020 B

Version

2

Bits

0b4cfcaa

Nonce

943,047,777

Timestamp

3/31/2018, 8:41:22 PM

Confirmations

4,232,860

Mined by

⛏️ P2SHAGiGmbbnc2iKCSy5KcRPZLERcUWib1dsLD

Merkle Root

7f0ff748b7fe6dd541655a0144127f4c994317d10f75fd081e2cf7f40c450e08
Transactions (2)
Coinbase69ac59e63cbef1…6961bfc9b0b24b
1 in β†’ 1 out7.8400 XPM110 B
AGiGmbbn…Wib1dsLD
88849ad562eae4…8de367aef90cca
5 in β†’ 2 out10702.1252 XPM820 B
AGsnUux8…doGehqHTAVa5dYbR…j5uZYCvt
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.

6.645 Γ— 10⁹³(94-digit number)
66457441356267020417…53789859021009337999
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
6.645 Γ— 10⁹³(94-digit number)
66457441356267020417…53789859021009337999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.329 Γ— 10⁹⁴(95-digit number)
13291488271253404083…07579718042018675999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.658 Γ— 10⁹⁴(95-digit number)
26582976542506808166…15159436084037351999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.316 Γ— 10⁹⁴(95-digit number)
53165953085013616333…30318872168074703999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.063 Γ— 10⁹⁡(96-digit number)
10633190617002723266…60637744336149407999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.126 Γ— 10⁹⁡(96-digit number)
21266381234005446533…21275488672298815999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.253 Γ— 10⁹⁡(96-digit number)
42532762468010893066…42550977344597631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.506 Γ— 10⁹⁡(96-digit number)
85065524936021786133…85101954689195263999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.701 Γ— 10⁹⁢(97-digit number)
17013104987204357226…70203909378390527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.402 Γ— 10⁹⁢(97-digit number)
34026209974408714453…40407818756781055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.805 Γ— 10⁹⁢(97-digit number)
68052419948817428907…80815637513562111999
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:57,862,641 XPMΒ·at block #6,827,315 Β· updates every 60s
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