XPM Prime Explorer symbol
XPMPrime Explorer

Block #488,585

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/12/2014, 6:57:44 PM Β· Difficulty 10.6574 Β· 6,315,070 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
07a612264395a543fe76816077e5f5ccdd596cbf74fff4bb424f5e95a9ad9f35
View on Chainz β†—

Height

#488,585

Difficulty

10.657446

Transactions

1

Size

186 B

Version

2

Bits

0aa84e65

Nonce

161,097

Timestamp

4/12/2014, 6:57:44 PM

Confirmations

6,315,070

Mined by

⛏️ taSI;AYCeLhqBJ84jFrKumsmd4mf6paeqGM6KK1

Merkle Root

eba533fe5fc3b5e1bebbd2e7636dac0b24a108f9c2fff2314950d950071947d6
Transactions (1)
Coinbaseeba533fe5fc3b5…50d950071947d6
1 in β†’ 1 out8.7900 XPM97 B
AYCeLhqB…eqGM6KK1
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.

2.711 Γ— 10⁹³(94-digit number)
27115321792684648937…64854202633870312601
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
2.711 Γ— 10⁹³(94-digit number)
27115321792684648937…64854202633870312601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.423 Γ— 10⁹³(94-digit number)
54230643585369297874…29708405267740625201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.084 Γ— 10⁹⁴(95-digit number)
10846128717073859574…59416810535481250401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.169 Γ— 10⁹⁴(95-digit number)
21692257434147719149…18833621070962500801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.338 Γ— 10⁹⁴(95-digit number)
43384514868295438299…37667242141925001601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.676 Γ— 10⁹⁴(95-digit number)
86769029736590876598…75334484283850003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.735 Γ— 10⁹⁡(96-digit number)
17353805947318175319…50668968567700006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.470 Γ— 10⁹⁡(96-digit number)
34707611894636350639…01337937135400012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.941 Γ— 10⁹⁡(96-digit number)
69415223789272701278…02675874270800025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.388 Γ— 10⁹⁢(97-digit number)
13883044757854540255…05351748541600051201
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:57,673,274 XPMΒ·at block #6,803,654 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK