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Block #1,534,768

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 11:18:18 AM Β· Difficulty 10.6181 Β· 5,281,732 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
932f9980ab3df21c53a9a803d3d42d61b55768c30b0af475040385d5c2fb1a36
View on Chainz β†—

Height

#1,534,768

Difficulty

10.618050

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e3887

Nonce

1,111,299,659

Timestamp

4/10/2016, 11:18:18 AM

Confirmations

5,281,732

Mined by

⛏️ P2SHANc1si5qHQP4UT5B1yr74djZ3e5gsx9WJt

Merkle Root

a73528d068ccf8027fce37c71a863adcd5917e0e5d1bcd8cb5e815f8b06fe933
Transactions (2)
Coinbase3c79dfb0a1d556…fa400571ed2fab
1 in β†’ 1 out8.9400 XPM110 B
ANc1si5q…5gsx9WJt
2d12d613a03cc8…dbf456a0d4dea1
51 in β†’ 1 out3156.4051 XPM7.41 KB
AQh2cDpo…3Mq9DLUp
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.

2.475 Γ— 10⁹⁢(97-digit number)
24750130662500147894…05541969033611527681
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
2.475 Γ— 10⁹⁢(97-digit number)
24750130662500147894…05541969033611527681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.950 Γ— 10⁹⁢(97-digit number)
49500261325000295789…11083938067223055361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.900 Γ— 10⁹⁢(97-digit number)
99000522650000591578…22167876134446110721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.980 Γ— 10⁹⁷(98-digit number)
19800104530000118315…44335752268892221441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.960 Γ— 10⁹⁷(98-digit number)
39600209060000236631…88671504537784442881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.920 Γ— 10⁹⁷(98-digit number)
79200418120000473262…77343009075568885761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.584 Γ— 10⁹⁸(99-digit number)
15840083624000094652…54686018151137771521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.168 Γ— 10⁹⁸(99-digit number)
31680167248000189305…09372036302275543041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.336 Γ— 10⁹⁸(99-digit number)
63360334496000378610…18744072604551086081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.267 Γ— 10⁹⁹(100-digit number)
12672066899200075722…37488145209102172161
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:57,776,129 XPMΒ·at block #6,816,499 Β· updates every 60s
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