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Block #3,038,993

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/4/2019, 9:51:31 PM Β· Difficulty 11.0130 Β· 3,801,649 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
56f7a5c2839a077e0dee8547b6319bdf2d823f1dac59605ecdcd96d29ba1c23d
View on Chainz β†—

Height

#3,038,993

Difficulty

11.013013

Transactions

2

Size

1.14 KB

Version

2

Bits

0b0354d9

Nonce

1,543,782,549

Timestamp

2/4/2019, 9:51:31 PM

Confirmations

3,801,649

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

f813e42fd00242767df000cb5cc73ef703a5fa6df07da2f9b323b0a4cdcc0d30
Transactions (2)
Coinbase11f2dfbf88378f…6e79d6e988c255
1 in β†’ 1 out8.2400 XPM110 B
AUMQRepm…tAfKmdW1
34b4c19bdea6df…d24e0f55b0f0c4
6 in β†’ 2 out946.4201 XPM966 B
AMcKwg1B…AG4RWhscANeo8URS…WrC2zfLb
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.

4.027 Γ— 10⁹⁴(95-digit number)
40278334823983790094…97352352622119820799
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
4.027 Γ— 10⁹⁴(95-digit number)
40278334823983790094…97352352622119820799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.027 Γ— 10⁹⁴(95-digit number)
40278334823983790094…97352352622119820801
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
8.055 Γ— 10⁹⁴(95-digit number)
80556669647967580189…94704705244239641599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.055 Γ— 10⁹⁴(95-digit number)
80556669647967580189…94704705244239641601
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
1.611 Γ— 10⁹⁡(96-digit number)
16111333929593516037…89409410488479283199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.611 Γ— 10⁹⁡(96-digit number)
16111333929593516037…89409410488479283201
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
3.222 Γ— 10⁹⁡(96-digit number)
32222667859187032075…78818820976958566399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.222 Γ— 10⁹⁡(96-digit number)
32222667859187032075…78818820976958566401
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
6.444 Γ— 10⁹⁡(96-digit number)
64445335718374064151…57637641953917132799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.444 Γ— 10⁹⁡(96-digit number)
64445335718374064151…57637641953917132801
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
1.288 Γ— 10⁹⁢(97-digit number)
12889067143674812830…15275283907834265599
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:57,969,477 XPMΒ·at block #6,840,641 Β· updates every 60s
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