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Block #661,256

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/3/2014, 9:13:30 PM Β· Difficulty 10.9563 Β· 6,137,333 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f044aded98e78665bcbc2715ed62c248be068f825534e2fec0d299df12bc2345
View on Chainz β†—

Height

#661,256

Difficulty

10.956324

Transactions

2

Size

579 B

Version

2

Bits

0af4d1a3

Nonce

83,378,150

Timestamp

8/3/2014, 9:13:30 PM

Confirmations

6,137,333

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d2971b084e696b545cc70f281136bc338f057190fe43f2c8bbdd959f149c7a9f
Transactions (2)
Coinbase34d17153023215…a449b733b8846d
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
82590a1427ade3…80249c59f98bdc
2 in β†’ 2 out2.9023 XPM373 B
AcoEo3Wf…ovQtGhRkAZB8PP99…1ge5rnCq
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.

1.940 Γ— 10⁹⁡(96-digit number)
19409687521354648423…21754811858919120801
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
1.940 Γ— 10⁹⁡(96-digit number)
19409687521354648423…21754811858919120801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.881 Γ— 10⁹⁡(96-digit number)
38819375042709296847…43509623717838241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.763 Γ— 10⁹⁡(96-digit number)
77638750085418593694…87019247435676483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.552 Γ— 10⁹⁢(97-digit number)
15527750017083718738…74038494871352966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.105 Γ— 10⁹⁢(97-digit number)
31055500034167437477…48076989742705932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.211 Γ— 10⁹⁢(97-digit number)
62111000068334874955…96153979485411865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.242 Γ— 10⁹⁷(98-digit number)
12422200013666974991…92307958970823731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.484 Γ— 10⁹⁷(98-digit number)
24844400027333949982…84615917941647462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.968 Γ— 10⁹⁷(98-digit number)
49688800054667899964…69231835883294924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.937 Γ— 10⁹⁷(98-digit number)
99377600109335799928…38463671766589849601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,632,725 XPMΒ·at block #6,798,588 Β· updates every 60s
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