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Block #2,112,205

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/12/2017, 1:08:36 AM Β· Difficulty 10.9017 Β· 4,729,061 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
81a06876c140238fd7d94dc787d2a96df847bbb1cc71a7d673f90d18d58dc939
View on Chainz β†—

Height

#2,112,205

Difficulty

10.901675

Transactions

2

Size

688 B

Version

2

Bits

0ae6d42a

Nonce

830,536,661

Timestamp

5/12/2017, 1:08:36 AM

Confirmations

4,729,061

Mined by

⛏️ P2SHAZqpJewygsYUZkj4Bg2oKzaypnyoaoKFPx

Merkle Root

89093bbafd2aae2e878eee707925753d61a538712b578548be9fd75b90161edb
Transactions (2)
Coinbaseb418b9261a65ad…d5248d31995e13
1 in β†’ 1 out8.4100 XPM109 B
AZqpJewy…yoaoKFPx
7cec39620237cb…60ac6492c902e7
3 in β†’ 1 out1499.9900 XPM489 B
AcxhUhX6…N8N8w2tm
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.

8.342 Γ— 10⁹³(94-digit number)
83420702538682314070…19823748787362687839
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
8.342 Γ— 10⁹³(94-digit number)
83420702538682314070…19823748787362687839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.342 Γ— 10⁹³(94-digit number)
83420702538682314070…19823748787362687841
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
1.668 Γ— 10⁹⁴(95-digit number)
16684140507736462814…39647497574725375679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.668 Γ— 10⁹⁴(95-digit number)
16684140507736462814…39647497574725375681
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
3.336 Γ— 10⁹⁴(95-digit number)
33368281015472925628…79294995149450751359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.336 Γ— 10⁹⁴(95-digit number)
33368281015472925628…79294995149450751361
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
6.673 Γ— 10⁹⁴(95-digit number)
66736562030945851256…58589990298901502719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.673 Γ— 10⁹⁴(95-digit number)
66736562030945851256…58589990298901502721
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
1.334 Γ— 10⁹⁡(96-digit number)
13347312406189170251…17179980597803005439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.334 Γ— 10⁹⁡(96-digit number)
13347312406189170251…17179980597803005441
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:57,974,493 XPMΒ·at block #6,841,265 Β· updates every 60s
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