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Block #403,461

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/14/2014, 5:04:52 AM Β· Difficulty 10.4287 Β· 6,422,844 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a342e1b8c3594bf7ed2f314734e8b4fd781b4d4607570f4b942e7e9e44981e92
View on Chainz β†—

Height

#403,461

Difficulty

10.428669

Transactions

1

Size

201 B

Version

2

Bits

0a6dbd3e

Nonce

64,286

Timestamp

2/14/2014, 5:04:52 AM

Confirmations

6,422,844

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

07eaef2534e15c2d74e38078aff434fa4645463b856aaed3dc7c6708343e1e7b
Transactions (1)
Coinbase07eaef2534e15c…7c6708343e1e7b
1 in β†’ 1 out9.1800 XPM110 B
AeKNrjNj…1NEq95Ta
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.

7.240 Γ— 10⁹⁢(97-digit number)
72408493283943624110…65284825537943746999
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
7.240 Γ— 10⁹⁢(97-digit number)
72408493283943624110…65284825537943746999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.448 Γ— 10⁹⁷(98-digit number)
14481698656788724822…30569651075887493999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.896 Γ— 10⁹⁷(98-digit number)
28963397313577449644…61139302151774987999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.792 Γ— 10⁹⁷(98-digit number)
57926794627154899288…22278604303549975999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.158 Γ— 10⁹⁸(99-digit number)
11585358925430979857…44557208607099951999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.317 Γ— 10⁹⁸(99-digit number)
23170717850861959715…89114417214199903999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.634 Γ— 10⁹⁸(99-digit number)
46341435701723919430…78228834428399807999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.268 Γ— 10⁹⁸(99-digit number)
92682871403447838861…56457668856799615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.853 Γ— 10⁹⁹(100-digit number)
18536574280689567772…12915337713599231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.707 Γ— 10⁹⁹(100-digit number)
37073148561379135544…25830675427198463999
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:57,854,579 XPMΒ·at block #6,826,304 Β· updates every 60s
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