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Block #2,434,410

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/21/2017, 4:01:40 PM Β· Difficulty 10.9176 Β· 4,404,761 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
06013d89775daee96d10729d59415568e054cea5b53f14beed0ec86648257609
View on Chainz β†—

Height

#2,434,410

Difficulty

10.917594

Transactions

2

Size

425 B

Version

2

Bits

0aeae76a

Nonce

1,341,390,991

Timestamp

12/21/2017, 4:01:40 PM

Confirmations

4,404,761

Mined by

⛏️ P2SHAHzYhKo8E7DQJWVvC5JDTSb6EDzcmXsVxa

Merkle Root

8434b6cf34fec8e74b926e86451b87d74a564fa37421ec6c412ecf4247b8b0a6
Transactions (2)
Coinbase0ea5fadbf5f87e…0497812b2f1b31
1 in β†’ 1 out8.3900 XPM109 B
AHzYhKo8…zcmXsVxa
3731cb894f4004…35d98fdbb575db
1 in β†’ 2 out90.8652 XPM226 B
AJT5ZDj4…DtnSSE5gAGirmLvD…MS7oSRts
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.

4.125 Γ— 10⁹⁴(95-digit number)
41258274644629489071…21176230402027971739
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
4.125 Γ— 10⁹⁴(95-digit number)
41258274644629489071…21176230402027971739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.251 Γ— 10⁹⁴(95-digit number)
82516549289258978143…42352460804055943479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.650 Γ— 10⁹⁡(96-digit number)
16503309857851795628…84704921608111886959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.300 Γ— 10⁹⁡(96-digit number)
33006619715703591257…69409843216223773919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.601 Γ— 10⁹⁡(96-digit number)
66013239431407182515…38819686432447547839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.320 Γ— 10⁹⁢(97-digit number)
13202647886281436503…77639372864895095679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.640 Γ— 10⁹⁢(97-digit number)
26405295772562873006…55278745729790191359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.281 Γ— 10⁹⁢(97-digit number)
52810591545125746012…10557491459580382719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.056 Γ— 10⁹⁷(98-digit number)
10562118309025149202…21114982919160765439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.112 Γ— 10⁹⁷(98-digit number)
21124236618050298404…42229965838321530879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.224 Γ— 10⁹⁷(98-digit number)
42248473236100596809…84459931676643061759
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:57,957,649 XPMΒ·at block #6,839,170 Β· updates every 60s
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