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Block #53,732

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 4:46:18 PM Β· Difficulty 8.9266 Β· 6,741,085 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
776f37ee8862b0fc9a3414cd15a21436160081a43b76e9957d5c68aa3eb5680d
View on Chainz β†—

Height

#53,732

Difficulty

8.926633

Transactions

1

Size

203 B

Version

2

Bits

08ed37d3

Nonce

547

Timestamp

7/16/2013, 4:46:18 PM

Confirmations

6,741,085

Mined by

⛏️ P2SHAGCUbq6Mxc7yQk3kiL3txXdSCgQSxWg1oL

Merkle Root

77824f364a8550f0deeaf8a07199fe693878402685deabbe81618b16f0c6d2a8
Transactions (1)
Coinbase77824f364a8550…618b16f0c6d2a8
1 in β†’ 1 out12.5300 XPM110 B
AGCUbq6M…QSxWg1oL
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.

4.788 Γ— 10¹⁰²(103-digit number)
47888643197312945687…48953489224076031161
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
4.788 Γ— 10¹⁰²(103-digit number)
47888643197312945687…48953489224076031161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.577 Γ— 10¹⁰²(103-digit number)
95777286394625891375…97906978448152062321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.915 Γ— 10¹⁰³(104-digit number)
19155457278925178275…95813956896304124641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.831 Γ— 10¹⁰³(104-digit number)
38310914557850356550…91627913792608249281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.662 Γ— 10¹⁰³(104-digit number)
76621829115700713100…83255827585216498561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.532 Γ— 10¹⁰⁴(105-digit number)
15324365823140142620…66511655170432997121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.064 Γ— 10¹⁰⁴(105-digit number)
30648731646280285240…33023310340865994241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.129 Γ— 10¹⁰⁴(105-digit number)
61297463292560570480…66046620681731988481
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:57,602,583 XPMΒ·at block #6,794,816 Β· updates every 60s
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