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Block #2,921,614

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/13/2018, 6:14:53 PM Β· Difficulty 11.3775 Β· 3,911,422 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
42b105ecf9a1983687714bef2bad9f45cbda11c61ab33421d686bf6e02f3cee6
View on Chainz β†—

Height

#2,921,614

Difficulty

11.377524

Transactions

2

Size

3.73 KB

Version

2

Bits

0b60a567

Nonce

838,951,743

Timestamp

11/13/2018, 6:14:53 PM

Confirmations

3,911,422

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

c6939add91693711f291412663db69f444edc2482ccf0d64bcbf9e8f7519d06b
Transactions (2)
Coinbase8b0706e85aded8…a76025517ff02c
1 in β†’ 1 out7.7500 XPM110 B
AUhjokok…k5m93PZR
6400015fcb1c76…5026643dfe2a79
24 in β†’ 2 out489.2387 XPM3.54 KB
AUXsuuFr…ZRJ8rpTUAYNGhdg5…y5SCmaE1
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.

4.984 Γ— 10⁹⁴(95-digit number)
49847664903450099327…61429246610175967359
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
4.984 Γ— 10⁹⁴(95-digit number)
49847664903450099327…61429246610175967359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.984 Γ— 10⁹⁴(95-digit number)
49847664903450099327…61429246610175967361
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
9.969 Γ— 10⁹⁴(95-digit number)
99695329806900198655…22858493220351934719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.969 Γ— 10⁹⁴(95-digit number)
99695329806900198655…22858493220351934721
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
1.993 Γ— 10⁹⁡(96-digit number)
19939065961380039731…45716986440703869439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.993 Γ— 10⁹⁡(96-digit number)
19939065961380039731…45716986440703869441
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
3.987 Γ— 10⁹⁡(96-digit number)
39878131922760079462…91433972881407738879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.987 Γ— 10⁹⁡(96-digit number)
39878131922760079462…91433972881407738881
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
7.975 Γ— 10⁹⁡(96-digit number)
79756263845520158924…82867945762815477759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.975 Γ— 10⁹⁡(96-digit number)
79756263845520158924…82867945762815477761
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
1.595 Γ— 10⁹⁢(97-digit number)
15951252769104031784…65735891525630955519
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:57,908,466 XPMΒ·at block #6,833,035 Β· updates every 60s
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