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Block #1,507,843

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/22/2016, 4:44:11 PM Β· Difficulty 10.6247 Β· 5,308,934 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
790f026483dc1cb01dfb100f9e5ee3061b5513fcba92f6ce19934bc682e18b80
View on Chainz β†—

Height

#1,507,843

Difficulty

10.624720

Transactions

2

Size

14.40 KB

Version

2

Bits

0a9fedaa

Nonce

409,207,963

Timestamp

3/22/2016, 4:44:11 PM

Confirmations

5,308,934

Mined by

⛏️ P2SHAeXt7Th7XfndqNxduye7jXsNoLGfbekCGE

Merkle Root

5cf13f6d9f9c557ffa865a6efef04abb0f562f8e7d2b5275f548546926e325f2
Transactions (2)
Coinbase1dbfe6fbb475e6…e8c592b0dc57ec
1 in β†’ 1 out9.1400 XPM109 B
AeXt7Th7…GfbekCGE
a62bfa4c5da4ec…38b6a16c102b5d
98 in β†’ 1 out81.0000 XPM14.21 KB
AW9z6iyE…ZMok5rfx
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.

1.391 Γ— 10⁹⁷(98-digit number)
13910446495695847011…16870481711882705921
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
1.391 Γ— 10⁹⁷(98-digit number)
13910446495695847011…16870481711882705921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.782 Γ— 10⁹⁷(98-digit number)
27820892991391694023…33740963423765411841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.564 Γ— 10⁹⁷(98-digit number)
55641785982783388046…67481926847530823681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.112 Γ— 10⁹⁸(99-digit number)
11128357196556677609…34963853695061647361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.225 Γ— 10⁹⁸(99-digit number)
22256714393113355218…69927707390123294721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.451 Γ— 10⁹⁸(99-digit number)
44513428786226710437…39855414780246589441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.902 Γ— 10⁹⁸(99-digit number)
89026857572453420875…79710829560493178881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.780 Γ— 10⁹⁹(100-digit number)
17805371514490684175…59421659120986357761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.561 Γ— 10⁹⁹(100-digit number)
35610743028981368350…18843318241972715521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.122 Γ— 10⁹⁹(100-digit number)
71221486057962736700…37686636483945431041
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:57,778,250 XPMΒ·at block #6,816,776 Β· updates every 60s
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