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Block #1,334,723

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/20/2015, 1:34:36 PM Β· Difficulty 10.8317 Β· 5,472,753 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d7adc4c2a9ea1428cc485463902074185d8cd495e75ac98d8517c8744894193d
View on Chainz β†—

Height

#1,334,723

Difficulty

10.831668

Transactions

2

Size

10.39 KB

Version

2

Bits

0ad4e82e

Nonce

157,963,799

Timestamp

11/20/2015, 1:34:36 PM

Confirmations

5,472,753

Mined by

⛏️ P2SHAP4KMJvQAFUUfiTSsrUvqN6NHPBRNDPSJw

Merkle Root

98ead474c19ca9cb7628672b08cbdf68b36c77362d887877eef58c7e049078d0
Transactions (2)
Coinbase57302186581747…b06b438cd906b1
1 in β†’ 1 out8.6400 XPM110 B
AP4KMJvQ…BRNDPSJw
8ec3ec520c6099…f1778c84bc8a8a
70 in β†’ 2 out1109.4250 XPM10.20 KB
AS8hfvj6…u5uXwtZsAR6vT1he…YS2pDXKC
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.

2.723 Γ— 10⁹⁴(95-digit number)
27235136366393508742…47878547950762414281
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
2.723 Γ— 10⁹⁴(95-digit number)
27235136366393508742…47878547950762414281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.447 Γ— 10⁹⁴(95-digit number)
54470272732787017484…95757095901524828561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.089 Γ— 10⁹⁡(96-digit number)
10894054546557403496…91514191803049657121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.178 Γ— 10⁹⁡(96-digit number)
21788109093114806993…83028383606099314241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.357 Γ— 10⁹⁡(96-digit number)
43576218186229613987…66056767212198628481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.715 Γ— 10⁹⁡(96-digit number)
87152436372459227975…32113534424397256961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.743 Γ— 10⁹⁢(97-digit number)
17430487274491845595…64227068848794513921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.486 Γ— 10⁹⁢(97-digit number)
34860974548983691190…28454137697589027841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.972 Γ— 10⁹⁢(97-digit number)
69721949097967382380…56908275395178055681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.394 Γ— 10⁹⁷(98-digit number)
13944389819593476476…13816550790356111361
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:57,703,834 XPMΒ·at block #6,807,475 Β· updates every 60s
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