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Block #960,443

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/3/2015, 11:53:26 PM Β· Difficulty 10.8857 Β· 5,842,725 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
959ef8e53762088f6cb6e36efd10d006324c8b211ac009e45c2fd0888d0ae26e
View on Chainz β†—

Height

#960,443

Difficulty

10.885684

Transactions

2

Size

432 B

Version

2

Bits

0ae2bc2b

Nonce

1,868,469,373

Timestamp

3/3/2015, 11:53:26 PM

Confirmations

5,842,725

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

fcad17e2ee4053200aa8e2990e4f248abb3848af293129ddbe8bed7bd08df7a0
Transactions (2)
Coinbase8b10d6a7eb8d18…05fa967e9ec1e2
1 in β†’ 1 out8.4400 XPM116 B
ANSXnLY2…Sd25TjkD
cea81ab00b75c6…51865ef782515e
1 in β†’ 2 out7.3573 XPM226 B
ARpjHv1k…4F9NvuWNAG2vzeDA…yX8D3GqW
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.

6.776 Γ— 10⁹⁴(95-digit number)
67760189652472439087…13831613200076648391
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
6.776 Γ— 10⁹⁴(95-digit number)
67760189652472439087…13831613200076648391
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.355 Γ— 10⁹⁡(96-digit number)
13552037930494487817…27663226400153296781
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.710 Γ— 10⁹⁡(96-digit number)
27104075860988975635…55326452800306593561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.420 Γ— 10⁹⁡(96-digit number)
54208151721977951270…10652905600613187121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.084 Γ— 10⁹⁢(97-digit number)
10841630344395590254…21305811201226374241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.168 Γ— 10⁹⁢(97-digit number)
21683260688791180508…42611622402452748481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.336 Γ— 10⁹⁢(97-digit number)
43366521377582361016…85223244804905496961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.673 Γ— 10⁹⁢(97-digit number)
86733042755164722032…70446489609810993921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.734 Γ— 10⁹⁷(98-digit number)
17346608551032944406…40892979219621987841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.469 Γ— 10⁹⁷(98-digit number)
34693217102065888812…81785958439243975681
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:57,669,360 XPMΒ·at block #6,803,167 Β· updates every 60s
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