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Block #2,656,804

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/11/2018, 9:31:15 AM Β· Difficulty 11.6839 Β· 4,180,993 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6feea9473af8cb7716f0f430cca194aa7830a22a8faa43a5be62ed95330eedb7
View on Chainz β†—

Height

#2,656,804

Difficulty

11.683936

Transactions

1

Size

200 B

Version

2

Bits

0baf1675

Nonce

740,764,279

Timestamp

5/11/2018, 9:31:15 AM

Confirmations

4,180,993

Mined by

⛏️ P2SHAKaHiL5kJPYL9Ldq2rz1St2xL7pzs3197J

Merkle Root

b79fdb4d1cfec0173a4dbdcaf7db54c9dae901b0ee8a4e155cd1d41c9db8ed44
Transactions (1)
Coinbaseb79fdb4d1cfec0…d1d41c9db8ed44
1 in β†’ 1 out7.3100 XPM110 B
AKaHiL5k…pzs3197J
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.

3.752 Γ— 10⁹³(94-digit number)
37524701754921954670…89944367027789714779
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
3.752 Γ— 10⁹³(94-digit number)
37524701754921954670…89944367027789714779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.504 Γ— 10⁹³(94-digit number)
75049403509843909341…79888734055579429559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.500 Γ— 10⁹⁴(95-digit number)
15009880701968781868…59777468111158859119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.001 Γ— 10⁹⁴(95-digit number)
30019761403937563736…19554936222317718239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.003 Γ— 10⁹⁴(95-digit number)
60039522807875127473…39109872444635436479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.200 Γ— 10⁹⁡(96-digit number)
12007904561575025494…78219744889270872959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.401 Γ— 10⁹⁡(96-digit number)
24015809123150050989…56439489778541745919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.803 Γ— 10⁹⁡(96-digit number)
48031618246300101978…12878979557083491839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.606 Γ— 10⁹⁡(96-digit number)
96063236492600203957…25757959114166983679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.921 Γ— 10⁹⁢(97-digit number)
19212647298520040791…51515918228333967359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.842 Γ— 10⁹⁢(97-digit number)
38425294597040081582…03031836456667934719
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:57,946,713 XPMΒ·at block #6,837,796 Β· updates every 60s
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