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Block #163,037

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/13/2013, 5:37:18 PM Β· Difficulty 9.8614 Β· 6,641,970 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fe43ca0bdd4d881295a706d4b07f0c1306e07a9acb1c1cbe688d27ffd4c75b11
View on Chainz β†—

Height

#163,037

Difficulty

9.861388

Transactions

1

Size

199 B

Version

2

Bits

09dc83ea

Nonce

37,594

Timestamp

9/13/2013, 5:37:18 PM

Confirmations

6,641,970

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

dddcf89e082f13c8c00228642c82e4369307aa1028dac2e49f7fd8993b279cad
Transactions (1)
Coinbasedddcf89e082f13…7fd8993b279cad
1 in β†’ 1 out10.2700 XPM109 B
AdDUNTYm…v4Zjqa77
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.

9.746 Γ— 10⁹⁴(95-digit number)
97468594106234420036…58708515577198536961
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
9.746 Γ— 10⁹⁴(95-digit number)
97468594106234420036…58708515577198536961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.949 Γ— 10⁹⁡(96-digit number)
19493718821246884007…17417031154397073921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.898 Γ— 10⁹⁡(96-digit number)
38987437642493768014…34834062308794147841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.797 Γ— 10⁹⁡(96-digit number)
77974875284987536029…69668124617588295681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.559 Γ— 10⁹⁢(97-digit number)
15594975056997507205…39336249235176591361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.118 Γ— 10⁹⁢(97-digit number)
31189950113995014411…78672498470353182721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.237 Γ— 10⁹⁢(97-digit number)
62379900227990028823…57344996940706365441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.247 Γ— 10⁹⁷(98-digit number)
12475980045598005764…14689993881412730881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.495 Γ— 10⁹⁷(98-digit number)
24951960091196011529…29379987762825461761
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:57,684,125 XPMΒ·at block #6,805,006 Β· updates every 60s
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