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Block #1,472,229

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/26/2016, 4:39:20 AM Β· Difficulty 10.6977 Β· 5,369,083 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a4159b51e083f9b355527cee4605620fe76f7bd3824e6c21b13fa4cd073e9386
View on Chainz β†—

Height

#1,472,229

Difficulty

10.697654

Transactions

2

Size

574 B

Version

2

Bits

0ab2996d

Nonce

967,149,606

Timestamp

2/26/2016, 4:39:20 AM

Confirmations

5,369,083

Mined by

⛏️ P2SHAYujWTY3P7wNUAyugb9vjyD8A5Np7CmzFP

Merkle Root

87ee58d4762da1705d176e4fe50a62b8c58a31be72d61ee77621c91958e054d6
Transactions (2)
Coinbaseefc52729861d79…7308aed61e93cd
1 in β†’ 1 out8.7300 XPM110 B
AYujWTY3…Np7CmzFP
839c4dd6fc9a39…baa11ea821ab5b
2 in β†’ 2 out4511.0921 XPM374 B
ANBTCNWp…v8EPJdRPAaEgFf4E…1aRMefQE
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.

8.000 Γ— 10⁹⁴(95-digit number)
80000824210991181747…72972502435513918401
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
8.000 Γ— 10⁹⁴(95-digit number)
80000824210991181747…72972502435513918401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.600 Γ— 10⁹⁡(96-digit number)
16000164842198236349…45945004871027836801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.200 Γ— 10⁹⁡(96-digit number)
32000329684396472698…91890009742055673601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.400 Γ— 10⁹⁡(96-digit number)
64000659368792945397…83780019484111347201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.280 Γ— 10⁹⁢(97-digit number)
12800131873758589079…67560038968222694401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.560 Γ— 10⁹⁢(97-digit number)
25600263747517178159…35120077936445388801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.120 Γ— 10⁹⁢(97-digit number)
51200527495034356318…70240155872890777601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.024 Γ— 10⁹⁷(98-digit number)
10240105499006871263…40480311745781555201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.048 Γ— 10⁹⁷(98-digit number)
20480210998013742527…80960623491563110401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.096 Γ— 10⁹⁷(98-digit number)
40960421996027485054…61921246983126220801
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:57,974,857 XPMΒ·at block #6,841,311 Β· updates every 60s
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