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Block #2,106,884

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/8/2017, 4:20:28 PM Β· Difficulty 10.8918 Β· 4,736,291 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9ac5be7135bb9f77fe1d8865ea314346ed0a6b794f2cc3d6e8201f4264e8cc61
View on Chainz β†—

Height

#2,106,884

Difficulty

10.891820

Transactions

2

Size

427 B

Version

2

Bits

0ae44e4c

Nonce

514,858,159

Timestamp

5/8/2017, 4:20:28 PM

Confirmations

4,736,291

Mined by

⛏️ P2SHAbS8DYdgdD2FK7KhJih8wYAmeDch2szjKY

Merkle Root

a234e6f17a8dba5c0be1048cd5f524a0d39436cf7aff18361157b0165ac6b330
Transactions (2)
Coinbasea28cb34c12c5bd…99923090a5b8cd
1 in β†’ 1 out8.4300 XPM110 B
AbS8DYdg…ch2szjKY
392fae1a48cd8b…1e4cceead0d948
1 in β†’ 2 out68091.3300 XPM227 B
AGXyT3wC…45xuWx2uAL7Pkj8P…4CRHUXVF
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.

1.213 Γ— 10⁹⁴(95-digit number)
12130711503180591051…85112816926870735001
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
1.213 Γ— 10⁹⁴(95-digit number)
12130711503180591051…85112816926870735001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.426 Γ— 10⁹⁴(95-digit number)
24261423006361182102…70225633853741470001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.852 Γ— 10⁹⁴(95-digit number)
48522846012722364204…40451267707482940001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.704 Γ— 10⁹⁴(95-digit number)
97045692025444728408…80902535414965880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.940 Γ— 10⁹⁡(96-digit number)
19409138405088945681…61805070829931760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.881 Γ— 10⁹⁡(96-digit number)
38818276810177891363…23610141659863520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.763 Γ— 10⁹⁡(96-digit number)
77636553620355782726…47220283319727040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.552 Γ— 10⁹⁢(97-digit number)
15527310724071156545…94440566639454080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.105 Γ— 10⁹⁢(97-digit number)
31054621448142313090…88881133278908160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.210 Γ— 10⁹⁢(97-digit number)
62109242896284626181…77762266557816320001
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:57,989,766 XPMΒ·at block #6,843,174 Β· updates every 60s
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