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Block #153,160

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2013, 7:42:57 PM Β· Difficulty 9.8631 Β· 6,657,692 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2e0e54bdc55d0e9d23dc1f64e48e258691539bebb0c9d237ab6717fc27c2f670
View on Chainz β†—

Height

#153,160

Difficulty

9.863111

Transactions

1

Size

200 B

Version

2

Bits

09dcf4df

Nonce

111,959

Timestamp

9/6/2013, 7:42:57 PM

Confirmations

6,657,692

Mined by

⛏️ P2SHAa6PpN3XWen9U28VLp3hDw33d6XAm9RHxt

Merkle Root

8496a132ddbdbcc95da1fb05f657d8885e3821c1593e451dcad5579b8c08ffaf
Transactions (1)
Coinbase8496a132ddbdbc…d5579b8c08ffaf
1 in β†’ 1 out10.2600 XPM109 B
Aa6PpN3X…XAm9RHxt
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.

2.889 Γ— 10⁹⁢(97-digit number)
28892813518592703608…23147084803815276801
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
2.889 Γ— 10⁹⁢(97-digit number)
28892813518592703608…23147084803815276801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.778 Γ— 10⁹⁢(97-digit number)
57785627037185407216…46294169607630553601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.155 Γ— 10⁹⁷(98-digit number)
11557125407437081443…92588339215261107201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.311 Γ— 10⁹⁷(98-digit number)
23114250814874162886…85176678430522214401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.622 Γ— 10⁹⁷(98-digit number)
46228501629748325772…70353356861044428801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.245 Γ— 10⁹⁷(98-digit number)
92457003259496651545…40706713722088857601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.849 Γ— 10⁹⁸(99-digit number)
18491400651899330309…81413427444177715201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.698 Γ— 10⁹⁸(99-digit number)
36982801303798660618…62826854888355430401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.396 Γ— 10⁹⁸(99-digit number)
73965602607597321236…25653709776710860801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.479 Γ— 10⁹⁹(100-digit number)
14793120521519464247…51307419553421721601
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:57,730,912 XPMΒ·at block #6,810,851 Β· updates every 60s
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