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Block #474,395

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/4/2014, 1:26:05 PM Β· Difficulty 10.4492 Β· 6,321,506 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a63215fc4d1771ec99e05a4b7d8830fb5e7a1b164b83ea86f5fbd9309279f994
View on Chainz β†—

Height

#474,395

Difficulty

10.449168

Transactions

2

Size

357 B

Version

2

Bits

0a72fca6

Nonce

46,043

Timestamp

4/4/2014, 1:26:05 PM

Confirmations

6,321,506

Mined by

⛏️ P2SHAQo5Sf84DcjUC65gbiaUvY1LDSCktZTnkR

Merkle Root

8a200058d4d95cb9159794bf8859ab0c562fd507437d1203bce49f8fbb469f44
Transactions (2)
Coinbase5024f1f9cd0cc7…d32382267c477c
1 in β†’ 1 out9.1500 XPM109 B
AQo5Sf84…CktZTnkR
8cf198c62889a8…bb92ecb3670516
1 in β†’ 1 out9.2000 XPM157 B
ATV4M1CV…dd9zw8nH
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.

8.715 Γ— 10⁹⁷(98-digit number)
87150388166386698583…26706680923256561181
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
8.715 Γ— 10⁹⁷(98-digit number)
87150388166386698583…26706680923256561181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.743 Γ— 10⁹⁸(99-digit number)
17430077633277339716…53413361846513122361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.486 Γ— 10⁹⁸(99-digit number)
34860155266554679433…06826723693026244721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.972 Γ— 10⁹⁸(99-digit number)
69720310533109358866…13653447386052489441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.394 Γ— 10⁹⁹(100-digit number)
13944062106621871773…27306894772104978881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.788 Γ— 10⁹⁹(100-digit number)
27888124213243743546…54613789544209957761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.577 Γ— 10⁹⁹(100-digit number)
55776248426487487093…09227579088419915521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.115 Γ— 10¹⁰⁰(101-digit number)
11155249685297497418…18455158176839831041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.231 Γ— 10¹⁰⁰(101-digit number)
22310499370594994837…36910316353679662081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.462 Γ— 10¹⁰⁰(101-digit number)
44620998741189989674…73820632707359324161
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:57,611,292 XPMΒ·at block #6,795,900 Β· updates every 60s
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