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Block #2,073,595

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/16/2017, 10:33:48 PM Β· Difficulty 10.8385 Β· 4,757,259 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e1d049ca953a0e09c4855a1d969d26a7087da7ac27e00864598c05d66df914fb
View on Chainz β†—

Height

#2,073,595

Difficulty

10.838458

Transactions

1

Size

208 B

Version

2

Bits

0ad6a533

Nonce

104,071,092

Timestamp

4/16/2017, 10:33:48 PM

Confirmations

4,757,259

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

4a47b8f59ec7092d6e0eab6b1d31a7532d6c5f99ea4c2bed2dfadfa39da1abf5
Transactions (1)
Coinbase4a47b8f59ec709…fadfa39da1abf5
1 in β†’ 1 out8.5000 XPM118 B
AM6GYpjw…aw86QDtR
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.

3.199 Γ— 10⁹⁴(95-digit number)
31997309737136613557…74448281666648758199
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
3.199 Γ— 10⁹⁴(95-digit number)
31997309737136613557…74448281666648758199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.399 Γ— 10⁹⁴(95-digit number)
63994619474273227114…48896563333297516399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.279 Γ— 10⁹⁡(96-digit number)
12798923894854645422…97793126666595032799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.559 Γ— 10⁹⁡(96-digit number)
25597847789709290845…95586253333190065599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.119 Γ— 10⁹⁡(96-digit number)
51195695579418581691…91172506666380131199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.023 Γ— 10⁹⁢(97-digit number)
10239139115883716338…82345013332760262399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.047 Γ— 10⁹⁢(97-digit number)
20478278231767432676…64690026665520524799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.095 Γ— 10⁹⁢(97-digit number)
40956556463534865353…29380053331041049599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.191 Γ— 10⁹⁢(97-digit number)
81913112927069730706…58760106662082099199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.638 Γ— 10⁹⁷(98-digit number)
16382622585413946141…17520213324164198399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.276 Γ— 10⁹⁷(98-digit number)
32765245170827892282…35040426648328396799
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:57,890,968 XPMΒ·at block #6,830,853 Β· updates every 60s
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