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Block #125,393

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2013, 5:24:06 AM Β· Difficulty 9.7769 Β· 6,701,914 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2cafff09ec863bc8a53790df912ed0e6175890becb5445ac6012d71da60aa752
View on Chainz β†—

Height

#125,393

Difficulty

9.776886

Transactions

1

Size

202 B

Version

2

Bits

09c6e1ff

Nonce

100,668,081

Timestamp

8/20/2013, 5:24:06 AM

Confirmations

6,701,914

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

8c6b43b6de9c358bc95a961012e78a293ad79daadaa8bda13ca9566cfdc790fd
Transactions (1)
Coinbase8c6b43b6de9c35…a9566cfdc790fd
1 in β†’ 1 out10.4500 XPM112 B
AT5A2KL6…CT16n6i2
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.

7.455 Γ— 10⁹⁴(95-digit number)
74553698243299388646…51486145684203441591
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
7.455 Γ— 10⁹⁴(95-digit number)
74553698243299388646…51486145684203441591
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.491 Γ— 10⁹⁡(96-digit number)
14910739648659877729…02972291368406883181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.982 Γ— 10⁹⁡(96-digit number)
29821479297319755458…05944582736813766361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.964 Γ— 10⁹⁡(96-digit number)
59642958594639510917…11889165473627532721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.192 Γ— 10⁹⁢(97-digit number)
11928591718927902183…23778330947255065441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.385 Γ— 10⁹⁢(97-digit number)
23857183437855804366…47556661894510130881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.771 Γ— 10⁹⁢(97-digit number)
47714366875711608733…95113323789020261761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.542 Γ— 10⁹⁢(97-digit number)
95428733751423217467…90226647578040523521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.908 Γ— 10⁹⁷(98-digit number)
19085746750284643493…80453295156081047041
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:57,862,568 XPMΒ·at block #6,827,306 Β· updates every 60s
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