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Block #2,472,654

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/14/2018, 12:22:43 PM Β· Difficulty 10.9629 Β· 4,367,760 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a89185c2fd6aceea8d70dee1589c5e9adb43a036e356f10af608929d7ff61bb0
View on Chainz β†—

Height

#2,472,654

Difficulty

10.962861

Transactions

2

Size

2.58 KB

Version

2

Bits

0af67e17

Nonce

1,128,771,863

Timestamp

1/14/2018, 12:22:43 PM

Confirmations

4,367,760

Mined by

⛏️ P2SHALuxPCRMpxXX2TE2xNQTZ4fXd69WrraA1V

Merkle Root

bc77e1532942493cfb0177b37cd2f50390b49752251c1f034b84609b820bb36c
Transactions (2)
Coinbase6e32bd049d897a…1e1b8b96aba6f6
1 in β†’ 1 out8.3400 XPM110 B
ALuxPCRM…9WrraA1V
05d9708aafb473…1b7b7f88e947fa
16 in β†’ 2 out116.1308 XPM2.39 KB
ARrjfR48…Tgspn3EuAGW8iVgz…xMg7SUHX
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.

5.692 Γ— 10⁹⁴(95-digit number)
56921674091237409522…71536950074825723521
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
5.692 Γ— 10⁹⁴(95-digit number)
56921674091237409522…71536950074825723521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.138 Γ— 10⁹⁡(96-digit number)
11384334818247481904…43073900149651447041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.276 Γ— 10⁹⁡(96-digit number)
22768669636494963808…86147800299302894081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.553 Γ— 10⁹⁡(96-digit number)
45537339272989927617…72295600598605788161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.107 Γ— 10⁹⁡(96-digit number)
91074678545979855235…44591201197211576321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.821 Γ— 10⁹⁢(97-digit number)
18214935709195971047…89182402394423152641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.642 Γ— 10⁹⁢(97-digit number)
36429871418391942094…78364804788846305281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.285 Γ— 10⁹⁢(97-digit number)
72859742836783884188…56729609577692610561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.457 Γ— 10⁹⁷(98-digit number)
14571948567356776837…13459219155385221121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.914 Γ— 10⁹⁷(98-digit number)
29143897134713553675…26918438310770442241
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:57,967,636 XPMΒ·at block #6,840,413 Β· updates every 60s
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