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Block #2,105,132

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/7/2017, 5:46:23 PM Β· Difficulty 10.8829 Β· 4,711,134 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
69acd0b5bb3725df5c6295645f617138de8d1b23a5e898bb1fb7d47ed22ecc6c
View on Chainz β†—

Height

#2,105,132

Difficulty

10.882876

Transactions

2

Size

41.28 KB

Version

2

Bits

0ae20430

Nonce

509,211,355

Timestamp

5/7/2017, 5:46:23 PM

Confirmations

4,711,134

Mined by

⛏️ P2SHASY71oBEwJvFHrd72HsrjLcT3WYhshYQAS

Merkle Root

f3ded62cac8011cf99889689acf2fd85323ff94f7b6330991ec34e43c65a4a14
Transactions (2)
Coinbasedda719c8a1e137…d46538d7851753
1 in β†’ 1 out8.9300 XPM109 B
ASY71oBE…YhshYQAS
31693f8268d0cf…f285cda5098c41
284 in β†’ 1 out83.2611 XPM41.09 KB
AKGxoSP8…8oH3hVLd
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.

4.322 Γ— 10⁹⁴(95-digit number)
43221907320165531814…80582247917252999479
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
4.322 Γ— 10⁹⁴(95-digit number)
43221907320165531814…80582247917252999479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.322 Γ— 10⁹⁴(95-digit number)
43221907320165531814…80582247917252999481
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
8.644 Γ— 10⁹⁴(95-digit number)
86443814640331063629…61164495834505998959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.644 Γ— 10⁹⁴(95-digit number)
86443814640331063629…61164495834505998961
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
1.728 Γ— 10⁹⁡(96-digit number)
17288762928066212725…22328991669011997919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.728 Γ— 10⁹⁡(96-digit number)
17288762928066212725…22328991669011997921
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
3.457 Γ— 10⁹⁡(96-digit number)
34577525856132425451…44657983338023995839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.457 Γ— 10⁹⁡(96-digit number)
34577525856132425451…44657983338023995841
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
6.915 Γ— 10⁹⁡(96-digit number)
69155051712264850903…89315966676047991679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.915 Γ— 10⁹⁡(96-digit number)
69155051712264850903…89315966676047991681
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:57,774,241 XPMΒ·at block #6,816,265 Β· updates every 60s
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