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Block #60,023

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2013, 5:34:15 AM Β· Difficulty 8.9675 Β· 6,736,037 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1472bb2ee4105b9199cae536b816ba6e2da75bb20b83cb66ab41dc303b2fb2ee
View on Chainz β†—

Height

#60,023

Difficulty

8.967499

Transactions

1

Size

199 B

Version

2

Bits

08f7ae01

Nonce

15

Timestamp

7/18/2013, 5:34:15 AM

Confirmations

6,736,037

Mined by

⛏️ P2SHAaRwLKz4rXapVtrfKzQ3ytjMoWskbMCFHM

Merkle Root

32c906cfcca2e85bb97b802b12a1c658d335f0c1f8a900244390ea66dd389b9d
Transactions (1)
Coinbase32c906cfcca2e8…90ea66dd389b9d
1 in β†’ 1 out12.4200 XPM109 B
AaRwLKz4…skbMCFHM
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.

5.469 Γ— 10⁹⁡(96-digit number)
54699220335839816862…95942134594785774331
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
5.469 Γ— 10⁹⁡(96-digit number)
54699220335839816862…95942134594785774331
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.093 Γ— 10⁹⁢(97-digit number)
10939844067167963372…91884269189571548661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.187 Γ— 10⁹⁢(97-digit number)
21879688134335926744…83768538379143097321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.375 Γ— 10⁹⁢(97-digit number)
43759376268671853489…67537076758286194641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.751 Γ— 10⁹⁢(97-digit number)
87518752537343706979…35074153516572389281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.750 Γ— 10⁹⁷(98-digit number)
17503750507468741395…70148307033144778561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.500 Γ— 10⁹⁷(98-digit number)
35007501014937482791…40296614066289557121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.001 Γ— 10⁹⁷(98-digit number)
70015002029874965583…80593228132579114241
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:57,612,576 XPMΒ·at block #6,796,059 Β· updates every 60s
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