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Block #359,809

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/15/2014, 1:12:24 AM Β· Difficulty 10.3882 Β· 6,465,222 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c62a7bb91169655e6a1680e19473221773496beb9f3dd353452b660eeb03f5b4
View on Chainz β†—

Height

#359,809

Difficulty

10.388205

Transactions

1

Size

199 B

Version

2

Bits

0a636167

Nonce

804,573

Timestamp

1/15/2014, 1:12:24 AM

Confirmations

6,465,222

Mined by

⛏️ P2SHAdRfXoAziafDMN3gvr8XtXUNewmh31AgUJ

Merkle Root

476370efefbf2d8c8387a1f7eb2536b0b93f7b725228fb514e03cfab2aba859e
Transactions (1)
Coinbase476370efefbf2d…03cfab2aba859e
1 in β†’ 1 out9.2500 XPM109 B
AdRfXoAz…mh31AgUJ
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.

2.717 Γ— 10⁹⁴(95-digit number)
27178643748440838172…64734007076661299199
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
2.717 Γ— 10⁹⁴(95-digit number)
27178643748440838172…64734007076661299199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.435 Γ— 10⁹⁴(95-digit number)
54357287496881676344…29468014153322598399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.087 Γ— 10⁹⁡(96-digit number)
10871457499376335268…58936028306645196799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.174 Γ— 10⁹⁡(96-digit number)
21742914998752670537…17872056613290393599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.348 Γ— 10⁹⁡(96-digit number)
43485829997505341075…35744113226580787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.697 Γ— 10⁹⁡(96-digit number)
86971659995010682151…71488226453161574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.739 Γ— 10⁹⁢(97-digit number)
17394331999002136430…42976452906323148799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.478 Γ— 10⁹⁢(97-digit number)
34788663998004272860…85952905812646297599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.957 Γ— 10⁹⁢(97-digit number)
69577327996008545721…71905811625292595199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.391 Γ— 10⁹⁷(98-digit number)
13915465599201709144…43811623250585190399
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:57,844,331 XPMΒ·at block #6,825,030 Β· updates every 60s
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