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Block #1,678,854

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2016, 6:54:00 PM Β· Difficulty 10.6967 Β· 5,136,001 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3e4e12eb0976f524b44fa49cd3f165a07c2daa158a984412737f866da716c795
View on Chainz β†—

Height

#1,678,854

Difficulty

10.696735

Transactions

2

Size

13.41 KB

Version

2

Bits

0ab25d40

Nonce

239,031,007

Timestamp

7/18/2016, 6:54:00 PM

Confirmations

5,136,001

Mined by

⛏️ P2SHAN23kS8Dz8UHg3Ut5p5hNNryECW2SaTm1P

Merkle Root

8afc972f15a5ec8cf6c387cab2f4c5765d2110c345d6f3babe6155c901df079d
Transactions (2)
Coinbase0bfc69738b966a…1329a92e768307
1 in β†’ 1 out8.8800 XPM109 B
AN23kS8D…W2SaTm1P
dac9a93231999f…86bfcd05dd7e11
91 in β†’ 2 out23.2266 XPM13.22 KB
ANZndfS1…DwiYDd2yAGyiGjWR…yy2Gk1HV
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.

5.981 Γ— 10⁹⁴(95-digit number)
59816797654677098018…71954630697386023481
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
5.981 Γ— 10⁹⁴(95-digit number)
59816797654677098018…71954630697386023481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.196 Γ— 10⁹⁡(96-digit number)
11963359530935419603…43909261394772046961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.392 Γ— 10⁹⁡(96-digit number)
23926719061870839207…87818522789544093921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.785 Γ— 10⁹⁡(96-digit number)
47853438123741678414…75637045579088187841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.570 Γ— 10⁹⁡(96-digit number)
95706876247483356828…51274091158176375681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.914 Γ— 10⁹⁢(97-digit number)
19141375249496671365…02548182316352751361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.828 Γ— 10⁹⁢(97-digit number)
38282750498993342731…05096364632705502721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.656 Γ— 10⁹⁢(97-digit number)
76565500997986685463…10192729265411005441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.531 Γ— 10⁹⁷(98-digit number)
15313100199597337092…20385458530822010881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.062 Γ— 10⁹⁷(98-digit number)
30626200399194674185…40770917061644021761
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:57,762,923 XPMΒ·at block #6,814,854 Β· updates every 60s
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