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Block #2,333,329

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/12/2017, 3:03:32 AM Β· Difficulty 10.9230 Β· 4,507,877 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a169531d58942517dbdca1f4537e92df0961eee20d9cdd792719b613a55f4883
View on Chainz β†—

Height

#2,333,329

Difficulty

10.922953

Transactions

1

Size

200 B

Version

2

Bits

0aec46a4

Nonce

366,247,045

Timestamp

10/12/2017, 3:03:32 AM

Confirmations

4,507,877

Mined by

⛏️ P2SHAH6fC7gq3Y5VyezLmUWnUdV1CQX94X16Bs

Merkle Root

cab4cd5dd41bfecaa1d9f70a4bcfd1e8db08e5c5748f3bed677632767bd8282e
Transactions (1)
Coinbasecab4cd5dd41bfe…7632767bd8282e
1 in β†’ 1 out8.3700 XPM110 B
AH6fC7gq…X94X16Bs
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.

4.414 Γ— 10⁹⁡(96-digit number)
44140000547286841041…41188506198782804799
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
4.414 Γ— 10⁹⁡(96-digit number)
44140000547286841041…41188506198782804799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.414 Γ— 10⁹⁡(96-digit number)
44140000547286841041…41188506198782804801
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
8.828 Γ— 10⁹⁡(96-digit number)
88280001094573682083…82377012397565609599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.828 Γ— 10⁹⁡(96-digit number)
88280001094573682083…82377012397565609601
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
1.765 Γ— 10⁹⁢(97-digit number)
17656000218914736416…64754024795131219199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.765 Γ— 10⁹⁢(97-digit number)
17656000218914736416…64754024795131219201
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
3.531 Γ— 10⁹⁢(97-digit number)
35312000437829472833…29508049590262438399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.531 Γ— 10⁹⁢(97-digit number)
35312000437829472833…29508049590262438401
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
7.062 Γ— 10⁹⁢(97-digit number)
70624000875658945667…59016099180524876799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.062 Γ— 10⁹⁢(97-digit number)
70624000875658945667…59016099180524876801
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:57,974,010 XPMΒ·at block #6,841,205 Β· updates every 60s
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