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Block #2,298,076

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/16/2017, 10:31:32 AM Β· Difficulty 10.9447 Β· 4,528,035 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a70ea0f009575f8e1bc5c207ba3968b86be6f3dd0900e91b50072eb79d426d96
View on Chainz β†—

Height

#2,298,076

Difficulty

10.944724

Transactions

2

Size

43.44 KB

Version

2

Bits

0af1d971

Nonce

1,669,188,020

Timestamp

9/16/2017, 10:31:32 AM

Confirmations

4,528,035

Mined by

⛏️ P2SHAcDWWQTmJ4uvmEx7iKz1h5gFN3aNRS4yMh

Merkle Root

4d38cde3855928588b0601fb91fa2b3e462ed44e58c648f0c9f6ad2e5d7866ca
Transactions (2)
Coinbasea5089e7c1ed892…e1a047d1594e52
1 in β†’ 1 out8.7800 XPM109 B
AcDWWQTm…aNRS4yMh
b0ee8d6877823d…c5560355df5be0
299 in β†’ 1 out273073.5876 XPM43.25 KB
ATNFg4tq…AMdaKJFH
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.

2.036 Γ— 10⁹⁴(95-digit number)
20364973014079954547…97251601672280718039
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
2.036 Γ— 10⁹⁴(95-digit number)
20364973014079954547…97251601672280718039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.036 Γ— 10⁹⁴(95-digit number)
20364973014079954547…97251601672280718041
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
4.072 Γ— 10⁹⁴(95-digit number)
40729946028159909094…94503203344561436079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.072 Γ— 10⁹⁴(95-digit number)
40729946028159909094…94503203344561436081
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
8.145 Γ— 10⁹⁴(95-digit number)
81459892056319818189…89006406689122872159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.145 Γ— 10⁹⁴(95-digit number)
81459892056319818189…89006406689122872161
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
1.629 Γ— 10⁹⁡(96-digit number)
16291978411263963637…78012813378245744319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.629 Γ— 10⁹⁡(96-digit number)
16291978411263963637…78012813378245744321
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
3.258 Γ— 10⁹⁡(96-digit number)
32583956822527927275…56025626756491488639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.258 Γ— 10⁹⁡(96-digit number)
32583956822527927275…56025626756491488641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.516 Γ— 10⁹⁡(96-digit number)
65167913645055854551…12051253512982977279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,853,012 XPMΒ·at block #6,826,110 Β· updates every 60s
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