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Block #1,568,548

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2016, 8:03:40 AM Β· Difficulty 10.7587 Β· 5,262,446 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9877f71bc7e240c4ec0e657ba202c72de5835c9bb11b23e4870d5939ca54671d
View on Chainz β†—

Height

#1,568,548

Difficulty

10.758654

Transactions

1

Size

200 B

Version

2

Bits

0ac2371f

Nonce

1,399,435,643

Timestamp

5/2/2016, 8:03:40 AM

Confirmations

5,262,446

Mined by

⛏️ P2SHAXRAuqBikVuEbYEJ1RMXp1QmE6f72nf1FD

Merkle Root

af78d77c10a101e5c630ad4571f35e7b4a5f825c66774f9c9da9d00bc22c6f28
Transactions (1)
Coinbaseaf78d77c10a101…a9d00bc22c6f28
1 in β†’ 1 out8.6300 XPM110 B
AXRAuqBi…f72nf1FD
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.

3.234 Γ— 10⁹⁴(95-digit number)
32340900642604955119…13027195036899586801
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
3.234 Γ— 10⁹⁴(95-digit number)
32340900642604955119…13027195036899586801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.468 Γ— 10⁹⁴(95-digit number)
64681801285209910238…26054390073799173601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.293 Γ— 10⁹⁡(96-digit number)
12936360257041982047…52108780147598347201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.587 Γ— 10⁹⁡(96-digit number)
25872720514083964095…04217560295196694401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.174 Γ— 10⁹⁡(96-digit number)
51745441028167928190…08435120590393388801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.034 Γ— 10⁹⁢(97-digit number)
10349088205633585638…16870241180786777601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.069 Γ— 10⁹⁢(97-digit number)
20698176411267171276…33740482361573555201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.139 Γ— 10⁹⁢(97-digit number)
41396352822534342552…67480964723147110401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.279 Γ— 10⁹⁢(97-digit number)
82792705645068685105…34961929446294220801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.655 Γ— 10⁹⁷(98-digit number)
16558541129013737021…69923858892588441601
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:57,892,093 XPMΒ·at block #6,830,993 Β· updates every 60s
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