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Block #256,452

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/11/2013, 8:40:25 PM Β· Difficulty 9.9751 Β· 6,550,518 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
93891cb4cb6f4016e8994b0e3a27817e5e8f9757d4c9e6e9609b6b91c455fe74
View on Chainz β†—

Height

#256,452

Difficulty

9.975133

Transactions

1

Size

200 B

Version

2

Bits

09f9a24b

Nonce

535,123

Timestamp

11/11/2013, 8:40:25 PM

Confirmations

6,550,518

Mined by

⛏️ P2SHAFv4GxfhFidL8Dd2giAFtoCmE3LfEWFx48

Merkle Root

f9b0743913daa74a0dfc89fcce24cc4b2a014e8cccaad8066482dda69d738fb7
Transactions (1)
Coinbasef9b0743913daa7…82dda69d738fb7
1 in β†’ 1 out10.0300 XPM109 B
AFv4Gxfh…LfEWFx48
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.

8.945 Γ— 10⁹⁷(98-digit number)
89452254377721233041…13450479597669602601
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
8.945 Γ— 10⁹⁷(98-digit number)
89452254377721233041…13450479597669602601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.789 Γ— 10⁹⁸(99-digit number)
17890450875544246608…26900959195339205201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.578 Γ— 10⁹⁸(99-digit number)
35780901751088493216…53801918390678410401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.156 Γ— 10⁹⁸(99-digit number)
71561803502176986433…07603836781356820801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.431 Γ— 10⁹⁹(100-digit number)
14312360700435397286…15207673562713641601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.862 Γ— 10⁹⁹(100-digit number)
28624721400870794573…30415347125427283201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.724 Γ— 10⁹⁹(100-digit number)
57249442801741589146…60830694250854566401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.144 Γ— 10¹⁰⁰(101-digit number)
11449888560348317829…21661388501709132801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.289 Γ— 10¹⁰⁰(101-digit number)
22899777120696635658…43322777003418265601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.579 Γ— 10¹⁰⁰(101-digit number)
45799554241393271317…86645554006836531201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.159 Γ— 10¹⁰⁰(101-digit number)
91599108482786542634…73291108013673062401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,699,860 XPMΒ·at block #6,806,969 Β· updates every 60s
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