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Block #2,129,993

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2017, 3:16:53 AM Β· Difficulty 10.9094 Β· 4,713,098 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
59b622a246fd642ee16ad6ea2c69aec3f46d067e68b2cdf2c912d146ec989080
View on Chainz β†—

Height

#2,129,993

Difficulty

10.909378

Transactions

1

Size

199 B

Version

2

Bits

0ae8cd03

Nonce

1,706,899,260

Timestamp

5/24/2017, 3:16:53 AM

Confirmations

4,713,098

Mined by

⛏️ P2SHAaFjcfU66Qdh7pvbZucGk2jirbgdt1fYzK

Merkle Root

c5c8aabe2636b649a1c3ff516588a77566f004db577a732346cd07bf3876489b
Transactions (1)
Coinbasec5c8aabe2636b6…cd07bf3876489b
1 in β†’ 1 out8.3900 XPM109 B
AaFjcfU6…gdt1fYzK
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.

2.227 Γ— 10⁹⁡(96-digit number)
22275704544064345134…57351977961958445439
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
2.227 Γ— 10⁹⁡(96-digit number)
22275704544064345134…57351977961958445439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.227 Γ— 10⁹⁡(96-digit number)
22275704544064345134…57351977961958445441
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
4.455 Γ— 10⁹⁡(96-digit number)
44551409088128690269…14703955923916890879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.455 Γ— 10⁹⁡(96-digit number)
44551409088128690269…14703955923916890881
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
8.910 Γ— 10⁹⁡(96-digit number)
89102818176257380538…29407911847833781759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.910 Γ— 10⁹⁡(96-digit number)
89102818176257380538…29407911847833781761
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
1.782 Γ— 10⁹⁢(97-digit number)
17820563635251476107…58815823695667563519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.782 Γ— 10⁹⁢(97-digit number)
17820563635251476107…58815823695667563521
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
3.564 Γ— 10⁹⁢(97-digit number)
35641127270502952215…17631647391335127039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.564 Γ— 10⁹⁢(97-digit number)
35641127270502952215…17631647391335127041
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:57,989,090 XPMΒ·at block #6,843,090 Β· updates every 60s
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