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Block #2,091,348

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2017, 10:51:54 AM Β· Difficulty 10.8725 Β· 4,733,707 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0636573bc89bb5c07a9cf2e6bb61b628f4288101c7c3c155be59eeb352b13795
View on Chainz β†—

Height

#2,091,348

Difficulty

10.872545

Transactions

2

Size

1.54 KB

Version

2

Bits

0adf5f1c

Nonce

1,416,462,814

Timestamp

4/28/2017, 10:51:54 AM

Confirmations

4,733,707

Mined by

⛏️ P2SHAXNNw755WzaE5a48NG6CSB3i1Lecxo6qJn

Merkle Root

a4fe7662a2e282113a979dfccf7a737c78a158c9b848d04a7e6039c09a1321dd
Transactions (2)
Coinbase28d4b76ffceaa9…7108eb87f65ff1
1 in β†’ 1 out8.4700 XPM110 B
AXNNw755…ecxo6qJn
afe514bd9bfb9e…217638a66d96c0
9 in β†’ 1 out293.6000 XPM1.34 KB
AXEZpwLv…Eyc7BaBc
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.

1.906 Γ— 10⁹⁡(96-digit number)
19061697499045719468…11357508354654781439
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
1.906 Γ— 10⁹⁡(96-digit number)
19061697499045719468…11357508354654781439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.906 Γ— 10⁹⁡(96-digit number)
19061697499045719468…11357508354654781441
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
3.812 Γ— 10⁹⁡(96-digit number)
38123394998091438937…22715016709309562879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.812 Γ— 10⁹⁡(96-digit number)
38123394998091438937…22715016709309562881
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
7.624 Γ— 10⁹⁡(96-digit number)
76246789996182877875…45430033418619125759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.624 Γ— 10⁹⁡(96-digit number)
76246789996182877875…45430033418619125761
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
1.524 Γ— 10⁹⁢(97-digit number)
15249357999236575575…90860066837238251519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.524 Γ— 10⁹⁢(97-digit number)
15249357999236575575…90860066837238251521
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
3.049 Γ— 10⁹⁢(97-digit number)
30498715998473151150…81720133674476503039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.049 Γ— 10⁹⁢(97-digit number)
30498715998473151150…81720133674476503041
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:57,844,525 XPMΒ·at block #6,825,054 Β· updates every 60s
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