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Block #133,915

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/25/2013, 6:55:26 PM Β· Difficulty 9.7987 Β· 6,693,320 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b4d9e918d754dcc01a6fabf25aefbefeff6511d8467d8ec3c89f6e39d807b144
View on Chainz β†—

Height

#133,915

Difficulty

9.798743

Transactions

2

Size

2.24 KB

Version

2

Bits

09cc7a6c

Nonce

80,958

Timestamp

8/25/2013, 6:55:26 PM

Confirmations

6,693,320

Mined by

⛏️ P2SHATiWLWYxRzqv4bxiE45A21efeh2Pst5qcn

Merkle Root

6fa22cc83c55cf9a444b454c1ac7d16310ff7e9d1ab5e849417bc4b3c30c535a
Transactions (2)
Coinbase3cd3f3e6a18a09…df3c28976cfd9d
1 in β†’ 1 out10.4300 XPM109 B
ATiWLWYx…2Pst5qcn
924a82520bb0fa…2764a98b68a566
18 in β†’ 1 out188.1300 XPM2.05 KB
AX7HepGv…Qm28ooHF
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.

3.881 Γ— 10⁹³(94-digit number)
38813101060480031862…05432275301920263641
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
3.881 Γ— 10⁹³(94-digit number)
38813101060480031862…05432275301920263641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.762 Γ— 10⁹³(94-digit number)
77626202120960063724…10864550603840527281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.552 Γ— 10⁹⁴(95-digit number)
15525240424192012744…21729101207681054561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.105 Γ— 10⁹⁴(95-digit number)
31050480848384025489…43458202415362109121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.210 Γ— 10⁹⁴(95-digit number)
62100961696768050979…86916404830724218241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.242 Γ— 10⁹⁡(96-digit number)
12420192339353610195…73832809661448436481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.484 Γ— 10⁹⁡(96-digit number)
24840384678707220391…47665619322896872961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.968 Γ— 10⁹⁡(96-digit number)
49680769357414440783…95331238645793745921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.936 Γ— 10⁹⁡(96-digit number)
99361538714828881567…90662477291587491841
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,861,980 XPMΒ·at block #6,827,234 Β· updates every 60s
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