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Block #143,447

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/31/2013, 4:02:53 PM Β· Difficulty 9.8374 Β· 6,690,186 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
52931608d473d08489a9f01832d9eb314a3bdcc17759d751b41b06d20da1f3ac
View on Chainz β†—

Height

#143,447

Difficulty

9.837368

Transactions

2

Size

688 B

Version

2

Bits

09d65dc5

Nonce

32,899

Timestamp

8/31/2013, 4:02:53 PM

Confirmations

6,690,186

Mined by

⛏️ P2SHAGZik86L64pGAaEh7nzzPQg2KSaSgH3sak

Merkle Root

9baac3bf77804c7740170058f6a6ff21f1330523841ed28a47ee6d0bec4b770e
Transactions (2)
Coinbase73aaa9e75c2e86…548952b43fcdd5
1 in β†’ 1 out10.3300 XPM109 B
AGZik86L…aSgH3sak
2174b412a3f370…e75f1938c39ff2
3 in β†’ 1 out681.8297 XPM489 B
AUbyxjzU…K2a5ibPv
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.

3.876 Γ— 10⁹³(94-digit number)
38762209717894868856…28145521115790704641
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
3.876 Γ— 10⁹³(94-digit number)
38762209717894868856…28145521115790704641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.752 Γ— 10⁹³(94-digit number)
77524419435789737712…56291042231581409281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.550 Γ— 10⁹⁴(95-digit number)
15504883887157947542…12582084463162818561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.100 Γ— 10⁹⁴(95-digit number)
31009767774315895084…25164168926325637121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.201 Γ— 10⁹⁴(95-digit number)
62019535548631790169…50328337852651274241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.240 Γ— 10⁹⁡(96-digit number)
12403907109726358033…00656675705302548481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.480 Γ— 10⁹⁡(96-digit number)
24807814219452716067…01313351410605096961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.961 Γ— 10⁹⁡(96-digit number)
49615628438905432135…02626702821210193921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.923 Γ— 10⁹⁡(96-digit number)
99231256877810864271…05253405642420387841
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:57,913,275 XPMΒ·at block #6,833,632 Β· updates every 60s
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