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Block #1,597,948

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2016, 10:45:09 AM Β· Difficulty 10.6099 Β· 5,243,316 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
364bbaabce5263a4a3ab003c7b160314dcc5c93147da82e68f7a3af5a77cb207
View on Chainz β†—

Height

#1,597,948

Difficulty

10.609891

Transactions

2

Size

1.14 KB

Version

2

Bits

0a9c21ce

Nonce

809,567,583

Timestamp

5/24/2016, 10:45:09 AM

Confirmations

5,243,316

Mined by

⛏️ P2SHAZZhh3Q2b48ijSjm5GGakZdwhWQgLxcoeH

Merkle Root

9bdd600cc91293570937ee8a7750b42bf69a326ab42eab9770b6c30921f0b0b3
Transactions (2)
Coinbase22eab6f792b3f5…a2ed43b480df89
1 in β†’ 1 out8.8800 XPM109 B
AZZhh3Q2…QgLxcoeH
1077b4e75bad45…875db270273a3b
6 in β†’ 2 out654.9324 XPM964 B
ATB74oXY…stL4TZyfAQiAqYg7…iFzp7ZPN
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.

1.831 Γ— 10⁹⁡(96-digit number)
18316281825567075443…11485041815713145001
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
1.831 Γ— 10⁹⁡(96-digit number)
18316281825567075443…11485041815713145001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.663 Γ— 10⁹⁡(96-digit number)
36632563651134150886…22970083631426290001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.326 Γ— 10⁹⁡(96-digit number)
73265127302268301773…45940167262852580001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.465 Γ— 10⁹⁢(97-digit number)
14653025460453660354…91880334525705160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.930 Γ— 10⁹⁢(97-digit number)
29306050920907320709…83760669051410320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.861 Γ— 10⁹⁢(97-digit number)
58612101841814641418…67521338102820640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.172 Γ— 10⁹⁷(98-digit number)
11722420368362928283…35042676205641280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.344 Γ— 10⁹⁷(98-digit number)
23444840736725856567…70085352411282560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.688 Γ— 10⁹⁷(98-digit number)
46889681473451713134…40170704822565120001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.377 Γ— 10⁹⁷(98-digit number)
93779362946903426269…80341409645130240001
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:57,974,476 XPMΒ·at block #6,841,263 Β· updates every 60s
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