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Block #48,560

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2013, 3:52:51 PM Β· Difficulty 8.8476 Β· 6,760,742 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c463861c3173f9725a3240ec1002e3c89c0df8dbd6591ee0afba82065475f0a0
View on Chainz β†—

Height

#48,560

Difficulty

8.847552

Transactions

2

Size

358 B

Version

2

Bits

08d8f92e

Nonce

469

Timestamp

7/15/2013, 3:52:51 PM

Confirmations

6,760,742

Mined by

⛏️ P2SHAX85bWR1s13thBJxnmv7Zr62AvX2GwLbPj

Merkle Root

0806fa760a6af3a2533a7f17be57d744c0472b9a61837de3ee1aeebf4925e587
Transactions (2)
Coinbase6bb164262140ee…fa4e28f1a1d871
1 in β†’ 1 out12.7700 XPM109 B
AX85bWR1…X2GwLbPj
f4b51745e1c646…648d5b8744d98b
1 in β†’ 1 out13.3400 XPM159 B
AUe28ERP…LtNhA52T
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.

1.095 Γ— 10⁹⁡(96-digit number)
10959699784474322754…02254142209230998401
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
1.095 Γ— 10⁹⁡(96-digit number)
10959699784474322754…02254142209230998401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.191 Γ— 10⁹⁡(96-digit number)
21919399568948645508…04508284418461996801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.383 Γ— 10⁹⁡(96-digit number)
43838799137897291017…09016568836923993601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.767 Γ— 10⁹⁡(96-digit number)
87677598275794582034…18033137673847987201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.753 Γ— 10⁹⁢(97-digit number)
17535519655158916406…36066275347695974401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.507 Γ— 10⁹⁢(97-digit number)
35071039310317832813…72132550695391948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.014 Γ— 10⁹⁢(97-digit number)
70142078620635665627…44265101390783897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.402 Γ— 10⁹⁷(98-digit number)
14028415724127133125…88530202781567795201
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:57,718,480 XPMΒ·at block #6,809,301 Β· updates every 60s
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