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Block #1,534,502

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 7:11:14 AM Β· Difficulty 10.6167 Β· 5,302,442 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a5d18919c9d308c03556cabe1ca06a50b2e38cfae4e3a6a44ae0433c5079ece
View on Chainz β†—

Height

#1,534,502

Difficulty

10.616731

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9de213

Nonce

76,647,161

Timestamp

4/10/2016, 7:11:14 AM

Confirmations

5,302,442

Mined by

⛏️ P2SHAd5mcqfNyaBPQjaY4smtrjzMPHD3cJdwpF

Merkle Root

786cbac7196a0b151106a757f8aae36538d594c61aabb38f9d2abbc4cca4bd97
Transactions (2)
Coinbaseb0415d54aa7e80…15a0ae0b806a24
1 in β†’ 1 out8.9400 XPM109 B
Ad5mcqfN…D3cJdwpF
5f301f7998ea9b…40817a6a7f53e7
51 in β†’ 1 out2762.8212 XPM7.41 KB
AVbHP3rF…Gprwmg7R
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.

4.595 Γ— 10⁹⁴(95-digit number)
45952995707737545316…10457053208291034241
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
4.595 Γ— 10⁹⁴(95-digit number)
45952995707737545316…10457053208291034241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.190 Γ— 10⁹⁴(95-digit number)
91905991415475090632…20914106416582068481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.838 Γ— 10⁹⁡(96-digit number)
18381198283095018126…41828212833164136961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.676 Γ— 10⁹⁡(96-digit number)
36762396566190036253…83656425666328273921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.352 Γ— 10⁹⁡(96-digit number)
73524793132380072506…67312851332656547841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.470 Γ— 10⁹⁢(97-digit number)
14704958626476014501…34625702665313095681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.940 Γ— 10⁹⁢(97-digit number)
29409917252952029002…69251405330626191361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.881 Γ— 10⁹⁢(97-digit number)
58819834505904058004…38502810661252382721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.176 Γ— 10⁹⁷(98-digit number)
11763966901180811600…77005621322504765441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.352 Γ— 10⁹⁷(98-digit number)
23527933802361623201…54011242645009530881
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:57,939,850 XPMΒ·at block #6,836,943 Β· updates every 60s
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