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Block #69,488

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 9:03:53 AM Β· Difficulty 8.9910 Β· 6,734,039 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
74dde90d1780715b21d54f64f5f6bfe71e686ace7ec4d02d62625a6a90a59470
View on Chainz β†—

Height

#69,488

Difficulty

8.990992

Transactions

1

Size

200 B

Version

2

Bits

08fdb1a2

Nonce

60

Timestamp

7/20/2013, 9:03:53 AM

Confirmations

6,734,039

Mined by

⛏️ P2SHAXSFye4rUycSu1xJ6pmwUfhCbvADf1YWCU

Merkle Root

7c4c65d0f7282b91062dce99a1be3de8e5b08cffa0bca302c674f1f6f23e8462
Transactions (1)
Coinbase7c4c65d0f7282b…74f1f6f23e8462
1 in β†’ 1 out12.3500 XPM110 B
AXSFye4r…ADf1YWCU
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.

2.227 Γ— 10⁹⁴(95-digit number)
22276787514428021402…84020172240640326401
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
2.227 Γ— 10⁹⁴(95-digit number)
22276787514428021402…84020172240640326401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.455 Γ— 10⁹⁴(95-digit number)
44553575028856042804…68040344481280652801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.910 Γ— 10⁹⁴(95-digit number)
89107150057712085609…36080688962561305601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.782 Γ— 10⁹⁡(96-digit number)
17821430011542417121…72161377925122611201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.564 Γ— 10⁹⁡(96-digit number)
35642860023084834243…44322755850245222401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.128 Γ— 10⁹⁡(96-digit number)
71285720046169668487…88645511700490444801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.425 Γ— 10⁹⁢(97-digit number)
14257144009233933697…77291023400980889601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.851 Γ— 10⁹⁢(97-digit number)
28514288018467867395…54582046801961779201
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:57,672,244 XPMΒ·at block #6,803,526 Β· updates every 60s
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