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Block #152,896

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2013, 3:23:16 PM Β· Difficulty 9.8630 Β· 6,664,242 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
18b0ff718c00c264c2f99f37390235f2733cc9391ff3ae51817eecd049067586
View on Chainz β†—

Height

#152,896

Difficulty

9.862976

Transactions

1

Size

198 B

Version

2

Bits

09dcec05

Nonce

63,122

Timestamp

9/6/2013, 3:23:16 PM

Confirmations

6,664,242

Mined by

⛏️ P2SHAQDX4A7fYRFPkMLMMFvDCVebjcjoSW2gJw

Merkle Root

37d382cd70c5babade00d41333fd9ea074db10b39699ff7f6f9049c997c26e82
Transactions (1)
Coinbase37d382cd70c5ba…9049c997c26e82
1 in β†’ 1 out10.2600 XPM109 B
AQDX4A7f…joSW2gJw
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.

2.841 Γ— 10⁹³(94-digit number)
28410716719736366480…35180231806534784001
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
2.841 Γ— 10⁹³(94-digit number)
28410716719736366480…35180231806534784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.682 Γ— 10⁹³(94-digit number)
56821433439472732960…70360463613069568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.136 Γ— 10⁹⁴(95-digit number)
11364286687894546592…40720927226139136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.272 Γ— 10⁹⁴(95-digit number)
22728573375789093184…81441854452278272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.545 Γ— 10⁹⁴(95-digit number)
45457146751578186368…62883708904556544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.091 Γ— 10⁹⁴(95-digit number)
90914293503156372737…25767417809113088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.818 Γ— 10⁹⁡(96-digit number)
18182858700631274547…51534835618226176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.636 Γ— 10⁹⁡(96-digit number)
36365717401262549094…03069671236452352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.273 Γ— 10⁹⁡(96-digit number)
72731434802525098189…06139342472904704001
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:57,781,139 XPMΒ·at block #6,817,137 Β· updates every 60s
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