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Block #2,439,903

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/25/2017, 5:22:14 AM Β· Difficulty 10.9236 Β· 4,377,131 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
525262ff331a603f3815f99d697de9dd3713490361a19fd71c390251829278a2
View on Chainz β†—

Height

#2,439,903

Difficulty

10.923634

Transactions

2

Size

1.14 KB

Version

2

Bits

0aec7346

Nonce

397,201,268

Timestamp

12/25/2017, 5:22:14 AM

Confirmations

4,377,131

Mined by

⛏️ P2SHAPcErscYpVnZKoK1zqG6Vz92HHuSBFCJDe

Merkle Root

a5881706f24c5f806c87e2a2f9f09545edd95ca8cef367accd88d1bd447489e0
Transactions (2)
Coinbase279b5d7d983417…762d5e8579430f
1 in β†’ 1 out8.3900 XPM109 B
APcErscY…uSBFCJDe
1672ff3228fe15…3e31b2398f7d0f
6 in β†’ 2 out549.5628 XPM964 B
AVZo9MVe…7MiGbh3AAdg6T8rP…ZN5JLJRp
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.

4.451 Γ— 10⁹⁴(95-digit number)
44518296008180404715…32343803789724728299
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
4.451 Γ— 10⁹⁴(95-digit number)
44518296008180404715…32343803789724728299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.903 Γ— 10⁹⁴(95-digit number)
89036592016360809431…64687607579449456599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.780 Γ— 10⁹⁡(96-digit number)
17807318403272161886…29375215158898913199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.561 Γ— 10⁹⁡(96-digit number)
35614636806544323772…58750430317797826399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.122 Γ— 10⁹⁡(96-digit number)
71229273613088647545…17500860635595652799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.424 Γ— 10⁹⁢(97-digit number)
14245854722617729509…35001721271191305599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.849 Γ— 10⁹⁢(97-digit number)
28491709445235459018…70003442542382611199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.698 Γ— 10⁹⁢(97-digit number)
56983418890470918036…40006885084765222399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.139 Γ— 10⁹⁷(98-digit number)
11396683778094183607…80013770169530444799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.279 Γ— 10⁹⁷(98-digit number)
22793367556188367214…60027540339060889599
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:57,780,303 XPMΒ·at block #6,817,033 Β· updates every 60s
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