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Block #2,978,092

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/23/2018, 11:05:20 AM Β· Difficulty 11.2881 Β· 3,863,372 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b1faad5dc8b2e62b6b886b0b0fd92fab71cbadbf219dff9731468798d907ae83
View on Chainz β†—

Height

#2,978,092

Difficulty

11.288117

Transactions

2

Size

5.91 KB

Version

2

Bits

0b49c206

Nonce

1,890,422,519

Timestamp

12/23/2018, 11:05:20 AM

Confirmations

3,863,372

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

6e3328ccf830a69cc2f82aa5b72e29e12444d4866e596842cabb6dac9877209a
Transactions (2)
Coinbase8149b9e9b5d2ae…11eb4ddc1c63a2
1 in β†’ 1 out7.9000 XPM110 B
AUMQRepm…tAfKmdW1
e76561656d1e55…385fc2ab1d77ec
39 in β†’ 2 out152.0600 XPM5.72 KB
AQRn6yfR…z5FsKtdjAUB9JhAy…xrAw1ZFS
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.

1.401 Γ— 10⁹⁴(95-digit number)
14019833943066501088…29766818154536166329
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
1.401 Γ— 10⁹⁴(95-digit number)
14019833943066501088…29766818154536166329
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.401 Γ— 10⁹⁴(95-digit number)
14019833943066501088…29766818154536166331
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
2.803 Γ— 10⁹⁴(95-digit number)
28039667886133002177…59533636309072332659
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.803 Γ— 10⁹⁴(95-digit number)
28039667886133002177…59533636309072332661
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
5.607 Γ— 10⁹⁴(95-digit number)
56079335772266004354…19067272618144665319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.607 Γ— 10⁹⁴(95-digit number)
56079335772266004354…19067272618144665321
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
1.121 Γ— 10⁹⁡(96-digit number)
11215867154453200870…38134545236289330639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.121 Γ— 10⁹⁡(96-digit number)
11215867154453200870…38134545236289330641
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
2.243 Γ— 10⁹⁡(96-digit number)
22431734308906401741…76269090472578661279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.243 Γ— 10⁹⁡(96-digit number)
22431734308906401741…76269090472578661281
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
4.486 Γ— 10⁹⁡(96-digit number)
44863468617812803483…52538180945157322559
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:57,976,085 XPMΒ·at block #6,841,463 Β· updates every 60s
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