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Block #2,943,889

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/29/2018, 3:13:19 AM Β· Difficulty 11.3948 Β· 3,872,259 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e4974c04adefa3b5c7f142c0f966ecc913c919b515985eb9059fae688889c4aa
View on Chainz β†—

Height

#2,943,889

Difficulty

11.394799

Transactions

2

Size

56.48 KB

Version

2

Bits

0b65118d

Nonce

939,923,481

Timestamp

11/29/2018, 3:13:19 AM

Confirmations

3,872,259

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

70f59b5a803151521b9f7579718c17f5b4e2dab59c9bfe97167fd44d274d3a2b
Transactions (2)
Coinbase5e263d4ac32687…1c1ae380f14d5f
1 in β†’ 1 out8.4700 XPM110 B
AbXwmGxD…4XXYP765
cbd2933499e862…0c148c32bb69e4
389 in β†’ 2 out30000.0104 XPM56.28 KB
AGQpME3k…55sp2K7iALPF8J52…Hjw4BMsG
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.

4.354 Γ— 10⁹⁴(95-digit number)
43542174225196111541…21292638111589358399
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
4.354 Γ— 10⁹⁴(95-digit number)
43542174225196111541…21292638111589358399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.354 Γ— 10⁹⁴(95-digit number)
43542174225196111541…21292638111589358401
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
8.708 Γ— 10⁹⁴(95-digit number)
87084348450392223083…42585276223178716799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.708 Γ— 10⁹⁴(95-digit number)
87084348450392223083…42585276223178716801
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
1.741 Γ— 10⁹⁡(96-digit number)
17416869690078444616…85170552446357433599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.741 Γ— 10⁹⁡(96-digit number)
17416869690078444616…85170552446357433601
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
3.483 Γ— 10⁹⁡(96-digit number)
34833739380156889233…70341104892714867199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.483 Γ— 10⁹⁡(96-digit number)
34833739380156889233…70341104892714867201
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
6.966 Γ— 10⁹⁡(96-digit number)
69667478760313778466…40682209785429734399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.966 Γ— 10⁹⁡(96-digit number)
69667478760313778466…40682209785429734401
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
1.393 Γ— 10⁹⁢(97-digit number)
13933495752062755693…81364419570859468799
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:57,773,305 XPMΒ·at block #6,816,147 Β· updates every 60s
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