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Block #972,922

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/13/2015, 7:08:42 PM Β· Difficulty 10.8421 Β· 5,832,947 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e1d5e230ad28831f98c82b9b6595d132072e0665cb242d77506418a046973b04
View on Chainz β†—

Height

#972,922

Difficulty

10.842104

Transactions

2

Size

1.14 KB

Version

2

Bits

0ad7941c

Nonce

592,009,018

Timestamp

3/13/2015, 7:08:42 PM

Confirmations

5,832,947

Mined by

⛏️ P2SHAZikdHwmi4Foz2yUjxhaokV6WHsfLTYGAd

Merkle Root

2988c22677cd5265038563d21800a1ef1280437dd41c7a15cacce8b2c0a3e395
Transactions (2)
Coinbase1edbc1cd4cf604…6245f9c97309a6
1 in β†’ 1 out8.5000 XPM110 B
AZikdHwm…sfLTYGAd
3ca6f28f5556cd…01f0f1f97757e5
6 in β†’ 2 out2575.6245 XPM965 B
AQhw1bo8…U9xpwjusARmq4LgH…Faq9WNdB
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.

4.709 Γ— 10⁹⁴(95-digit number)
47098992985338966779…98012733860574185159
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
4.709 Γ— 10⁹⁴(95-digit number)
47098992985338966779…98012733860574185159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.709 Γ— 10⁹⁴(95-digit number)
47098992985338966779…98012733860574185161
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
9.419 Γ— 10⁹⁴(95-digit number)
94197985970677933559…96025467721148370319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.419 Γ— 10⁹⁴(95-digit number)
94197985970677933559…96025467721148370321
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
1.883 Γ— 10⁹⁡(96-digit number)
18839597194135586711…92050935442296740639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.883 Γ— 10⁹⁡(96-digit number)
18839597194135586711…92050935442296740641
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
3.767 Γ— 10⁹⁡(96-digit number)
37679194388271173423…84101870884593481279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.767 Γ— 10⁹⁡(96-digit number)
37679194388271173423…84101870884593481281
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
7.535 Γ— 10⁹⁡(96-digit number)
75358388776542346847…68203741769186962559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.535 Γ— 10⁹⁡(96-digit number)
75358388776542346847…68203741769186962561
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:57,691,035 XPMΒ·at block #6,805,868 Β· updates every 60s
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