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Block #883,870

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/6/2015, 2:38:47 AM Β· Difficulty 10.9588 Β· 5,933,951 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
071374a15ee5a968b553c31b5cfc2b6bfd12c7b532a456b2f3106f7cb7c47999
View on Chainz β†—

Height

#883,870

Difficulty

10.958824

Transactions

3

Size

880 B

Version

2

Bits

0af57578

Nonce

1,679,402,534

Timestamp

1/6/2015, 2:38:47 AM

Confirmations

5,933,951

Mined by

⛏️ P2SHATjjK5YiwRDfphRW2j7zdVhz9GHNjsi1GY

Merkle Root

bfa33150ffa7dfb32eedc06e7d0737b3b213a92657309408d4a5db35b5381ab4
Transactions (3)
Coinbasecaadee839c42a3…d4d8eb0bdeb830
1 in β†’ 1 out8.3300 XPM109 B
ATjjK5Yi…HNjsi1GY
7024b2017c1cc3…debcdf96a2bbfb
2 in β†’ 1 out2.0001 XPM342 B
AHUGQf6X…kT4kuj3U
5ef0d9c56a0287…da5b0e2d79a13e
2 in β†’ 1 out7.9900 XPM339 B
AHM5nWRo…724RKRRp
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.

1.318 Γ— 10⁹⁡(96-digit number)
13185515792440319336…83203759975320045201
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
1.318 Γ— 10⁹⁡(96-digit number)
13185515792440319336…83203759975320045201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.637 Γ— 10⁹⁡(96-digit number)
26371031584880638672…66407519950640090401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.274 Γ— 10⁹⁡(96-digit number)
52742063169761277344…32815039901280180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.054 Γ— 10⁹⁢(97-digit number)
10548412633952255468…65630079802560361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.109 Γ— 10⁹⁢(97-digit number)
21096825267904510937…31260159605120723201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.219 Γ— 10⁹⁢(97-digit number)
42193650535809021875…62520319210241446401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.438 Γ— 10⁹⁢(97-digit number)
84387301071618043750…25040638420482892801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.687 Γ— 10⁹⁷(98-digit number)
16877460214323608750…50081276840965785601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.375 Γ— 10⁹⁷(98-digit number)
33754920428647217500…00162553681931571201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.750 Γ— 10⁹⁷(98-digit number)
67509840857294435000…00325107363863142401
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:57,786,631 XPMΒ·at block #6,817,820 Β· updates every 60s
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