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Block #1,523,838

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/3/2016, 12:41:22 AM Β· Difficulty 10.6006 Β· 5,292,474 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7391e900dd38f5640b77489a22ea703d2688228d69665c1507cda9d77d752a10
View on Chainz β†—

Height

#1,523,838

Difficulty

10.600577

Transactions

2

Size

539 B

Version

2

Bits

0a99bf69

Nonce

1,251,617,699

Timestamp

4/3/2016, 12:41:22 AM

Confirmations

5,292,474

Mined by

⛏️ P2SHAQP7psKeXBQ7G7aH5G8VFyj44dE4Z7wXzd

Merkle Root

528b9f26e570113d8486e7153f94d3e58014bb06ab97bc4900c18126e2d05ed0
Transactions (2)
Coinbase64a59525eb1508…7abb63bf39f3d8
1 in β†’ 1 out8.9000 XPM109 B
AQP7psKe…E4Z7wXzd
e16c04dad6e227…cbc19bba86a8c7
2 in β†’ 1 out20.0000 XPM340 B
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.

1.913 Γ— 10⁹⁴(95-digit number)
19131838251270837829…90582355340990766081
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
1.913 Γ— 10⁹⁴(95-digit number)
19131838251270837829…90582355340990766081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.826 Γ— 10⁹⁴(95-digit number)
38263676502541675659…81164710681981532161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.652 Γ— 10⁹⁴(95-digit number)
76527353005083351319…62329421363963064321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.530 Γ— 10⁹⁡(96-digit number)
15305470601016670263…24658842727926128641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.061 Γ— 10⁹⁡(96-digit number)
30610941202033340527…49317685455852257281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.122 Γ— 10⁹⁡(96-digit number)
61221882404066681055…98635370911704514561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.224 Γ— 10⁹⁢(97-digit number)
12244376480813336211…97270741823409029121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.448 Γ— 10⁹⁢(97-digit number)
24488752961626672422…94541483646818058241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.897 Γ— 10⁹⁢(97-digit number)
48977505923253344844…89082967293636116481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.795 Γ— 10⁹⁢(97-digit number)
97955011846506689688…78165934587272232961
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:57,774,615 XPMΒ·at block #6,816,311 Β· updates every 60s
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