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Block #2,925,097

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/16/2018, 7:18:07 AM Β· Difficulty 11.3548 Β· 3,914,254 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0b62868679f8f502cd1ef38f5acebb5b67a5e4053f882a2ca6f44a152c28ed71
View on Chainz β†—

Height

#2,925,097

Difficulty

11.354837

Transactions

1

Size

201 B

Version

2

Bits

0b5ad69a

Nonce

354,055,928

Timestamp

11/16/2018, 7:18:07 AM

Confirmations

3,914,254

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

f88e9e5b85aee3564ed07e2933827be1ffd80cf8a559f7574a3dffba92eaba83
Transactions (1)
Coinbasef88e9e5b85aee3…3dffba92eaba83
1 in β†’ 1 out7.7400 XPM110 B
AbXwmGxD…4XXYP765
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.

1.766 Γ— 10⁹⁢(97-digit number)
17660066746421061822…36361497336842719999
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
1.766 Γ— 10⁹⁢(97-digit number)
17660066746421061822…36361497336842719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.532 Γ— 10⁹⁢(97-digit number)
35320133492842123644…72722994673685439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.064 Γ— 10⁹⁢(97-digit number)
70640266985684247288…45445989347370879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.412 Γ— 10⁹⁷(98-digit number)
14128053397136849457…90891978694741759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.825 Γ— 10⁹⁷(98-digit number)
28256106794273698915…81783957389483519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.651 Γ— 10⁹⁷(98-digit number)
56512213588547397830…63567914778967039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.130 Γ— 10⁹⁸(99-digit number)
11302442717709479566…27135829557934079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.260 Γ— 10⁹⁸(99-digit number)
22604885435418959132…54271659115868159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.520 Γ— 10⁹⁸(99-digit number)
45209770870837918264…08543318231736319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.041 Γ— 10⁹⁸(99-digit number)
90419541741675836528…17086636463472639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.808 Γ— 10⁹⁹(100-digit number)
18083908348335167305…34173272926945279999
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:57,959,094 XPMΒ·at block #6,839,350 Β· updates every 60s
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