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Block #48,896

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2013, 5:31:39 PM Β· Difficulty 8.8546 Β· 6,756,365 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
db1749e79f4a58ea56d76925b58de567f1a9014e87240f90fb62ad8d1eefde79
View on Chainz β†—

Height

#48,896

Difficulty

8.854567

Transactions

1

Size

200 B

Version

2

Bits

08dac4e3

Nonce

50

Timestamp

7/15/2013, 5:31:39 PM

Confirmations

6,756,365

Mined by

⛏️ P2SHAX85bWR1s13thBJxnmv7Zr62AvX2GwLbPj

Merkle Root

ef93fd04d8bbcbc077991fc8e6f11972b6d0e69c66d0d58ae93329dd2f965656
Transactions (1)
Coinbaseef93fd04d8bbcb…3329dd2f965656
1 in β†’ 1 out12.7400 XPM110 B
AX85bWR1…X2GwLbPj
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.

3.321 Γ— 10⁹⁴(95-digit number)
33212610294920804443…47182312113041184601
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
3.321 Γ— 10⁹⁴(95-digit number)
33212610294920804443…47182312113041184601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.642 Γ— 10⁹⁴(95-digit number)
66425220589841608886…94364624226082369201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.328 Γ— 10⁹⁡(96-digit number)
13285044117968321777…88729248452164738401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.657 Γ— 10⁹⁡(96-digit number)
26570088235936643554…77458496904329476801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.314 Γ— 10⁹⁡(96-digit number)
53140176471873287109…54916993808658953601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.062 Γ— 10⁹⁢(97-digit number)
10628035294374657421…09833987617317907201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.125 Γ— 10⁹⁢(97-digit number)
21256070588749314843…19667975234635814401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.251 Γ— 10⁹⁢(97-digit number)
42512141177498629687…39335950469271628801
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:57,686,158 XPMΒ·at block #6,805,260 Β· updates every 60s
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