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Block #1,410,514

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/12/2016, 6:20:04 PM Β· Difficulty 10.8052 Β· 5,427,897 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
37ed3ed9e198a4737d934d56f338a78e5a3324143e0a0a58b778ada649ab4d13
View on Chainz β†—

Height

#1,410,514

Difficulty

10.805226

Transactions

2

Size

2.01 KB

Version

2

Bits

0ace2351

Nonce

162,558,872

Timestamp

1/12/2016, 6:20:04 PM

Confirmations

5,427,897

Mined by

⛏️ P2SHAcCPZjtgZrvqRLnQgrvUFxpxzBQsMvye4Z

Merkle Root

e9df1cafc7ede9814ac24011278a7560164b0501151bdf99f1aaf193c6ae616a
Transactions (2)
Coinbase66a6de2fb23f6d…2c71eaab091751
1 in β†’ 1 out8.6000 XPM109 B
AcCPZjtg…QsMvye4Z
a14660d74b95c6…2b6c3c093ec233
12 in β†’ 2 out48.7754 XPM1.82 KB
ARJUAwG8…5huRS93kAVRcUdqu…1jNf74CA
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.

1.140 Γ— 10⁹⁡(96-digit number)
11400187192933172016…52154193702764392001
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
1.140 Γ— 10⁹⁡(96-digit number)
11400187192933172016…52154193702764392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.280 Γ— 10⁹⁡(96-digit number)
22800374385866344032…04308387405528784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.560 Γ— 10⁹⁡(96-digit number)
45600748771732688064…08616774811057568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.120 Γ— 10⁹⁡(96-digit number)
91201497543465376129…17233549622115136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.824 Γ— 10⁹⁢(97-digit number)
18240299508693075225…34467099244230272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.648 Γ— 10⁹⁢(97-digit number)
36480599017386150451…68934198488460544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.296 Γ— 10⁹⁢(97-digit number)
72961198034772300903…37868396976921088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.459 Γ— 10⁹⁷(98-digit number)
14592239606954460180…75736793953842176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.918 Γ— 10⁹⁷(98-digit number)
29184479213908920361…51473587907684352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.836 Γ— 10⁹⁷(98-digit number)
58368958427817840723…02947175815368704001
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:57,951,560 XPMΒ·at block #6,838,410 Β· updates every 60s
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