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Block #2,440,556

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/25/2017, 3:04:50 PM Β· Difficulty 10.9247 Β· 4,398,762 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fc43d33ef86d43cda593620892c88f399bfce24572246a4a728393118cdd2811
View on Chainz β†—

Height

#2,440,556

Difficulty

10.924682

Transactions

2

Size

1.57 KB

Version

2

Bits

0aecb7f6

Nonce

2,038,891,172

Timestamp

12/25/2017, 3:04:50 PM

Confirmations

4,398,762

Mined by

⛏️ P2SHAZ1aWhP1jxWnAGZWfrjL1jahYeiTbWPDaf

Merkle Root

0a497edac7fbcbceec911a8c3ea755bdb9c7f6a446351af231e353be7efc5688
Transactions (2)
Coinbase4be0e035f84dca…6ba1222c202130
1 in β†’ 1 out8.3900 XPM110 B
AZ1aWhP1…iTbWPDaf
353365eca6b606…6e6d003df6e045
9 in β†’ 2 out1280.0015 XPM1.38 KB
Ab976B9S…wHF4BrJfAKGnFxH4…tKyWyfun
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.

1.299 Γ— 10⁹⁴(95-digit number)
12997842571899203428…48114763897643865559
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
1.299 Γ— 10⁹⁴(95-digit number)
12997842571899203428…48114763897643865559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.599 Γ— 10⁹⁴(95-digit number)
25995685143798406856…96229527795287731119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.199 Γ— 10⁹⁴(95-digit number)
51991370287596813712…92459055590575462239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.039 Γ— 10⁹⁡(96-digit number)
10398274057519362742…84918111181150924479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.079 Γ— 10⁹⁡(96-digit number)
20796548115038725485…69836222362301848959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.159 Γ— 10⁹⁡(96-digit number)
41593096230077450970…39672444724603697919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.318 Γ— 10⁹⁡(96-digit number)
83186192460154901940…79344889449207395839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.663 Γ— 10⁹⁢(97-digit number)
16637238492030980388…58689778898414791679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.327 Γ— 10⁹⁢(97-digit number)
33274476984061960776…17379557796829583359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.654 Γ— 10⁹⁢(97-digit number)
66548953968123921552…34759115593659166719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,958,825 XPMΒ·at block #6,839,317 Β· updates every 60s
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