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Block #2,131,691

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/25/2017, 6:49:09 AM Β· Difficulty 10.9103 Β· 4,682,626 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6d591295035926e7394854a17feff5f160aff8e91963749501d4e2291880f6d1
View on Chainz β†—

Height

#2,131,691

Difficulty

10.910259

Transactions

2

Size

427 B

Version

2

Bits

0ae906bc

Nonce

593,997,442

Timestamp

5/25/2017, 6:49:09 AM

Confirmations

4,682,626

Mined by

⛏️ P2SHAbtfiscYWUPEpqu1XkfZrfZwakJScW95mw

Merkle Root

bce9ab6de707f38a7d91ac73fa5e889705b149dd3bce0fc30939a522f28fe6d2
Transactions (2)
Coinbaseb1996081a41d1f…7fa94c78d176e1
1 in β†’ 1 out8.4000 XPM110 B
AbtfiscY…JScW95mw
399dbd46368f24…7ad06e180abca5
1 in β†’ 2 out112417.8024 XPM227 B
AGCgM4Sr…xt6W9vCpAco5jEWw…84wuGZvs
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.

1.945 Γ— 10⁹⁴(95-digit number)
19459074379538192015…15840782699374315839
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
1.945 Γ— 10⁹⁴(95-digit number)
19459074379538192015…15840782699374315839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.891 Γ— 10⁹⁴(95-digit number)
38918148759076384030…31681565398748631679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.783 Γ— 10⁹⁴(95-digit number)
77836297518152768060…63363130797497263359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.556 Γ— 10⁹⁡(96-digit number)
15567259503630553612…26726261594994526719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.113 Γ— 10⁹⁡(96-digit number)
31134519007261107224…53452523189989053439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.226 Γ— 10⁹⁡(96-digit number)
62269038014522214448…06905046379978106879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.245 Γ— 10⁹⁢(97-digit number)
12453807602904442889…13810092759956213759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.490 Γ— 10⁹⁢(97-digit number)
24907615205808885779…27620185519912427519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.981 Γ— 10⁹⁢(97-digit number)
49815230411617771559…55240371039824855039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.963 Γ— 10⁹⁢(97-digit number)
99630460823235543118…10480742079649710079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.992 Γ— 10⁹⁷(98-digit number)
19926092164647108623…20961484159299420159
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:57,758,599 XPMΒ·at block #6,814,316 Β· updates every 60s
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