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Block #287,856

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/1/2013, 12:09:55 PM Β· Difficulty 9.9871 Β· 6,514,775 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
325c702241bf555a7a533f4d605dae0be833563b6ac6e1e62d2880f975f2d1ff
View on Chainz β†—

Height

#287,856

Difficulty

9.987109

Transactions

1

Size

201 B

Version

2

Bits

09fcb327

Nonce

43,068

Timestamp

12/1/2013, 12:09:55 PM

Confirmations

6,514,775

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c0edd7e0d420c0df7b72c0303579744377ed35439958479653c4f6cacb6c6682
Transactions (1)
Coinbasec0edd7e0d420c0…c4f6cacb6c6682
1 in β†’ 1 out10.0100 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.

1.861 Γ— 10⁹⁢(97-digit number)
18618169524504251461…13620066389611192321
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.861 Γ— 10⁹⁢(97-digit number)
18618169524504251461…13620066389611192321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.723 Γ— 10⁹⁢(97-digit number)
37236339049008502923…27240132779222384641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.447 Γ— 10⁹⁢(97-digit number)
74472678098017005847…54480265558444769281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.489 Γ— 10⁹⁷(98-digit number)
14894535619603401169…08960531116889538561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.978 Γ— 10⁹⁷(98-digit number)
29789071239206802339…17921062233779077121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.957 Γ— 10⁹⁷(98-digit number)
59578142478413604678…35842124467558154241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.191 Γ— 10⁹⁸(99-digit number)
11915628495682720935…71684248935116308481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.383 Γ— 10⁹⁸(99-digit number)
23831256991365441871…43368497870232616961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.766 Γ— 10⁹⁸(99-digit number)
47662513982730883742…86736995740465233921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.532 Γ— 10⁹⁸(99-digit number)
95325027965461767485…73473991480930467841
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,665,063 XPMΒ·at block #6,802,630 Β· updates every 60s
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