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Block #2,097,155

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2017, 11:09:51 AM Β· Difficulty 10.8735 Β· 4,730,075 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6df13d3996633ca8b7c9857691cfdb8d3549d05c65354f293a22d3f4abebcfea
View on Chainz β†—

Height

#2,097,155

Difficulty

10.873478

Transactions

2

Size

983 B

Version

2

Bits

0adf9c3a

Nonce

760,199,897

Timestamp

5/2/2017, 11:09:51 AM

Confirmations

4,730,075

Mined by

⛏️ P2SHAVG2cAGVrkBGxC7K1h9Qx3eGQbDLXWr76k

Merkle Root

1673dbba7bf0da036e30fe4310fffe833048026922aca1d70c041c62c663305a
Transactions (2)
Coinbase259ecf2ec00cc7…952efc37b5ded7
1 in β†’ 1 out8.4700 XPM110 B
AVG2cAGV…DLXWr76k
73f06c2a76a4f3…d9959af562a737
5 in β†’ 1 out3006.9900 XPM783 B
AZAUpPRK…y6qkZdaT
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.

3.462 Γ— 10⁹⁴(95-digit number)
34625007233679743540…34567956355527588719
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
3.462 Γ— 10⁹⁴(95-digit number)
34625007233679743540…34567956355527588719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.925 Γ— 10⁹⁴(95-digit number)
69250014467359487081…69135912711055177439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.385 Γ— 10⁹⁡(96-digit number)
13850002893471897416…38271825422110354879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.770 Γ— 10⁹⁡(96-digit number)
27700005786943794832…76543650844220709759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.540 Γ— 10⁹⁡(96-digit number)
55400011573887589665…53087301688441419519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.108 Γ— 10⁹⁢(97-digit number)
11080002314777517933…06174603376882839039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.216 Γ— 10⁹⁢(97-digit number)
22160004629555035866…12349206753765678079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.432 Γ— 10⁹⁢(97-digit number)
44320009259110071732…24698413507531356159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.864 Γ— 10⁹⁢(97-digit number)
88640018518220143464…49396827015062712319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.772 Γ— 10⁹⁷(98-digit number)
17728003703644028692…98793654030125424639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.545 Γ— 10⁹⁷(98-digit number)
35456007407288057385…97587308060250849279
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:57,861,940 XPMΒ·at block #6,827,229 Β· updates every 60s
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