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Block #2,266,077

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/24/2017, 4:31:04 PM Β· Difficulty 10.9514 Β· 4,576,032 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
7b3a4121813f154b6c84b5d4a22f4af4738019844b431cec97d65a85a956b2e7
View on Chainz β†—

Height

#2,266,077

Difficulty

10.951415

Transactions

1

Size

200 B

Version

2

Bits

0af38fec

Nonce

1,588,904,266

Timestamp

8/24/2017, 4:31:04 PM

Confirmations

4,576,032

Mined by

⛏️ P2SHAGymt5uFhS4apsMRmqWHhef8tVoNsTBV3L

Merkle Root

a4c1113ffade552158ce92f6d09bdeaa2e755c3a5d94b32a930ca9b7d36c20f6
Transactions (1)
Coinbasea4c1113ffade55…0ca9b7d36c20f6
1 in β†’ 1 out8.3200 XPM110 B
AGymt5uF…oNsTBV3L
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.

4.693 Γ— 10⁹⁴(95-digit number)
46939361572081684101…23632251879072428639
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
4.693 Γ— 10⁹⁴(95-digit number)
46939361572081684101…23632251879072428639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.693 Γ— 10⁹⁴(95-digit number)
46939361572081684101…23632251879072428641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
9.387 Γ— 10⁹⁴(95-digit number)
93878723144163368202…47264503758144857279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.387 Γ— 10⁹⁴(95-digit number)
93878723144163368202…47264503758144857281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.877 Γ— 10⁹⁡(96-digit number)
18775744628832673640…94529007516289714559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.877 Γ— 10⁹⁡(96-digit number)
18775744628832673640…94529007516289714561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
3.755 Γ— 10⁹⁡(96-digit number)
37551489257665347280…89058015032579429119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.755 Γ— 10⁹⁡(96-digit number)
37551489257665347280…89058015032579429121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
7.510 Γ— 10⁹⁡(96-digit number)
75102978515330694561…78116030065158858239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.510 Γ— 10⁹⁡(96-digit number)
75102978515330694561…78116030065158858241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,981,260 XPMΒ·at block #6,842,108 Β· updates every 60s
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