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Block #391,209

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/5/2014, 4:04:20 PM Β· Difficulty 10.4298 Β· 6,424,756 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f4e4f3a28c6e41bd7836fba1c6e836e76727d0cbc771b5a77791a272fa308a19
View on Chainz β†—

Height

#391,209

Difficulty

10.429758

Transactions

1

Size

199 B

Version

2

Bits

0a6e049f

Nonce

58,549

Timestamp

2/5/2014, 4:04:20 PM

Confirmations

6,424,756

Mined by

⛏️ P2SHAcH2s7Y4D9hVCSQQdA7jo9e2ue1nk8yDe6

Merkle Root

57aca57cd175d69b0f86ffedfbb713a230659ce711228be0ec523ce8592531b8
Transactions (1)
Coinbase57aca57cd175d6…523ce8592531b8
1 in β†’ 1 out9.1800 XPM109 B
AcH2s7Y4…1nk8yDe6
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.

2.695 Γ— 10⁹³(94-digit number)
26957948884464347563…26436375989652915281
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
2.695 Γ— 10⁹³(94-digit number)
26957948884464347563…26436375989652915281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.391 Γ— 10⁹³(94-digit number)
53915897768928695126…52872751979305830561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.078 Γ— 10⁹⁴(95-digit number)
10783179553785739025…05745503958611661121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.156 Γ— 10⁹⁴(95-digit number)
21566359107571478050…11491007917223322241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.313 Γ— 10⁹⁴(95-digit number)
43132718215142956101…22982015834446644481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.626 Γ— 10⁹⁴(95-digit number)
86265436430285912202…45964031668893288961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.725 Γ— 10⁹⁡(96-digit number)
17253087286057182440…91928063337786577921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.450 Γ— 10⁹⁡(96-digit number)
34506174572114364880…83856126675573155841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.901 Γ— 10⁹⁡(96-digit number)
69012349144228729761…67712253351146311681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.380 Γ— 10⁹⁢(97-digit number)
13802469828845745952…35424506702292623361
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:57,771,831 XPMΒ·at block #6,815,964 Β· updates every 60s
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