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Block #153,331

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2013, 10:25:10 PM Β· Difficulty 9.8633 Β· 6,653,743 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fe3419786e60dc31025cad80b327fbf98ed5fe0b43d7aefc788ffd8217e588f8
View on Chainz β†—

Height

#153,331

Difficulty

9.863333

Transactions

2

Size

391 B

Version

2

Bits

09dd036a

Nonce

72,983

Timestamp

9/6/2013, 10:25:10 PM

Confirmations

6,653,743

Mined by

⛏️ P2SHAdrYVTm6tX9eRqNDg18gVHTNxMUkrsrMvD

Merkle Root

1a7e621a69ec2decdd327b1e02f6b724ba32a36c323be9b53171496f7bab8562
Transactions (2)
Coinbase8bf2810cb023ac…2c39f9e0233ca9
1 in β†’ 1 out10.2700 XPM109 B
AdrYVTm6…UkrsrMvD
a12c21126dc0d4…9d832aba30ceef
1 in β†’ 1 out191.1000 XPM191 B
AXqLdXqC…P4VUDvUP
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.

2.735 Γ— 10⁹⁢(97-digit number)
27351943705630714772…34482089342572967361
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
2.735 Γ— 10⁹⁢(97-digit number)
27351943705630714772…34482089342572967361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.470 Γ— 10⁹⁢(97-digit number)
54703887411261429545…68964178685145934721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.094 Γ— 10⁹⁷(98-digit number)
10940777482252285909…37928357370291869441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.188 Γ— 10⁹⁷(98-digit number)
21881554964504571818…75856714740583738881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.376 Γ— 10⁹⁷(98-digit number)
43763109929009143636…51713429481167477761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.752 Γ— 10⁹⁷(98-digit number)
87526219858018287272…03426858962334955521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.750 Γ— 10⁹⁸(99-digit number)
17505243971603657454…06853717924669911041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.501 Γ— 10⁹⁸(99-digit number)
35010487943207314909…13707435849339822081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.002 Γ— 10⁹⁸(99-digit number)
70020975886414629818…27414871698679644161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.400 Γ— 10⁹⁹(100-digit number)
14004195177282925963…54829743397359288321
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:57,700,687 XPMΒ·at block #6,807,073 Β· updates every 60s
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