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Block #255,745

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/11/2013, 10:30:25 AM Β· Difficulty 9.9746 Β· 6,553,039 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
16a2e8dabd2b987bd30525cc5ca03bfee0e6a7870169f4a05763f056c9828e68
View on Chainz β†—

Height

#255,745

Difficulty

9.974631

Transactions

1

Size

199 B

Version

2

Bits

09f9816a

Nonce

12,361

Timestamp

11/11/2013, 10:30:25 AM

Confirmations

6,553,039

Mined by

⛏️ P2SHAFv4GxfhFidL8Dd2giAFtoCmE3LfEWFx48

Merkle Root

cbe4b2a160db1c0dc24baf531f795511d50a45a92fa1adcdf54a9ff06ef3333c
Transactions (1)
Coinbasecbe4b2a160db1c…4a9ff06ef3333c
1 in β†’ 1 out10.0400 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.

1.554 Γ— 10⁹⁡(96-digit number)
15548060637230114888…75825374089491781121
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
1.554 Γ— 10⁹⁡(96-digit number)
15548060637230114888…75825374089491781121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.109 Γ— 10⁹⁡(96-digit number)
31096121274460229777…51650748178983562241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.219 Γ— 10⁹⁡(96-digit number)
62192242548920459554…03301496357967124481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.243 Γ— 10⁹⁢(97-digit number)
12438448509784091910…06602992715934248961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.487 Γ— 10⁹⁢(97-digit number)
24876897019568183821…13205985431868497921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.975 Γ— 10⁹⁢(97-digit number)
49753794039136367643…26411970863736995841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.950 Γ— 10⁹⁢(97-digit number)
99507588078272735287…52823941727473991681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.990 Γ— 10⁹⁷(98-digit number)
19901517615654547057…05647883454947983361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.980 Γ— 10⁹⁷(98-digit number)
39803035231309094114…11295766909895966721
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:57,714,323 XPMΒ·at block #6,808,783 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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