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Block #1,393,516

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/31/2015, 8:41:17 PM Β· Difficulty 10.8101 Β· 5,415,462 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c08b9258c70e9ca52531b95ab5cbce432ed5cc62d4458b80bb7b64e859d89354
View on Chainz β†—

Height

#1,393,516

Difficulty

10.810094

Transactions

2

Size

12.70 KB

Version

2

Bits

0acf6253

Nonce

1,135,491,353

Timestamp

12/31/2015, 8:41:17 PM

Confirmations

5,415,462

Mined by

⛏️ P2SHAJx3qD2yLqFtWebeU7TfKxGFtfwF7cpfpU

Merkle Root

8c174abfd2ed7ab3acf3550de67bd3e97576e082b0cfc2275e50aa42fe35b132
Transactions (2)
Coinbasedc8b386cc11b58…0ebc7d960aa8b4
1 in β†’ 1 out8.6700 XPM110 B
AJx3qD2y…wF7cpfpU
a47d4a423fdd4c…f9f51b88562e06
86 in β†’ 2 out74.6250 XPM12.50 KB
AHVkps1J…t8nMGMwPAcMpew3F…1yR4JhRa
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.

3.083 Γ— 10⁹⁴(95-digit number)
30836406939329249496…19349052003649873161
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
3.083 Γ— 10⁹⁴(95-digit number)
30836406939329249496…19349052003649873161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.167 Γ— 10⁹⁴(95-digit number)
61672813878658498992…38698104007299746321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.233 Γ— 10⁹⁡(96-digit number)
12334562775731699798…77396208014599492641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.466 Γ— 10⁹⁡(96-digit number)
24669125551463399596…54792416029198985281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.933 Γ— 10⁹⁡(96-digit number)
49338251102926799193…09584832058397970561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.867 Γ— 10⁹⁡(96-digit number)
98676502205853598387…19169664116795941121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.973 Γ— 10⁹⁢(97-digit number)
19735300441170719677…38339328233591882241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.947 Γ— 10⁹⁢(97-digit number)
39470600882341439355…76678656467183764481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.894 Γ— 10⁹⁢(97-digit number)
78941201764682878710…53357312934367528961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.578 Γ— 10⁹⁷(98-digit number)
15788240352936575742…06714625868735057921
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:57,715,880 XPMΒ·at block #6,808,977 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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