XPM Prime Explorer symbol
XPMPrime Explorer

Block #49,339

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2013, 7:52:40 PM Β· Difficulty 8.8630 Β· 6,747,540 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
041f4b6ee44415dbb992b726bd351e3874674431a436ffa1e0993cf7ea365cfe
View on Chainz β†—

Height

#49,339

Difficulty

8.863039

Transactions

1

Size

200 B

Version

2

Bits

08dcf01d

Nonce

1,105

Timestamp

7/15/2013, 7:52:40 PM

Confirmations

6,747,540

Mined by

⛏️ P2SHAcjhaVoWPPShdSp4K3fBKNtTx1hAPjZTBV

Merkle Root

073792a52e56f0afa1237aa555f6389b44095f276f0f4ed2795b99c6914eb8e6
Transactions (1)
Coinbase073792a52e56f0…5b99c6914eb8e6
1 in β†’ 1 out12.7100 XPM110 B
AcjhaVoW…hAPjZTBV
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.

1.318 Γ— 10⁹⁴(95-digit number)
13187799884737282706…68285835421378283101
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
1.318 Γ— 10⁹⁴(95-digit number)
13187799884737282706…68285835421378283101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.637 Γ— 10⁹⁴(95-digit number)
26375599769474565412…36571670842756566201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.275 Γ— 10⁹⁴(95-digit number)
52751199538949130825…73143341685513132401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.055 Γ— 10⁹⁡(96-digit number)
10550239907789826165…46286683371026264801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.110 Γ— 10⁹⁡(96-digit number)
21100479815579652330…92573366742052529601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.220 Γ— 10⁹⁡(96-digit number)
42200959631159304660…85146733484105059201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.440 Γ— 10⁹⁡(96-digit number)
84401919262318609321…70293466968210118401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.688 Γ— 10⁹⁢(97-digit number)
16880383852463721864…40586933936420236801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,619,048 XPMΒ·at block #6,796,878 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