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Block #3,412,475

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2019, 6:53:17 AM Β· Difficulty 10.9850 Β· 3,429,800 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
923728f404e1c3229d95b79b6f87c98cd2056c9adada3caf4148765b85d7927f
View on Chainz β†—

Height

#3,412,475

Difficulty

10.984959

Transactions

1

Size

201 B

Version

2

Bits

0afc264e

Nonce

175,105,527

Timestamp

10/30/2019, 6:53:17 AM

Confirmations

3,429,800

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

3dc048dd8993c4db804224a94c595212592f465225f4d14c4ce801be1c47efa9
Transactions (1)
Coinbase3dc048dd8993c4…e801be1c47efa9
1 in β†’ 1 out8.2700 XPM110 B
ASiq2qtK…VMhmk7yL
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.

1.998 Γ— 10⁹⁢(97-digit number)
19980637118461463606…02203358517006317599
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
1.998 Γ— 10⁹⁢(97-digit number)
19980637118461463606…02203358517006317599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.998 Γ— 10⁹⁢(97-digit number)
19980637118461463606…02203358517006317601
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
3.996 Γ— 10⁹⁢(97-digit number)
39961274236922927213…04406717034012635199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.996 Γ— 10⁹⁢(97-digit number)
39961274236922927213…04406717034012635201
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
7.992 Γ— 10⁹⁢(97-digit number)
79922548473845854426…08813434068025270399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.992 Γ— 10⁹⁢(97-digit number)
79922548473845854426…08813434068025270401
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
1.598 Γ— 10⁹⁷(98-digit number)
15984509694769170885…17626868136050540799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.598 Γ— 10⁹⁷(98-digit number)
15984509694769170885…17626868136050540801
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
3.196 Γ— 10⁹⁷(98-digit number)
31969019389538341770…35253736272101081599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.196 Γ— 10⁹⁷(98-digit number)
31969019389538341770…35253736272101081601
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
6.393 Γ— 10⁹⁷(98-digit number)
63938038779076683540…70507472544202163199
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:57,982,601 XPMΒ·at block #6,842,274 Β· updates every 60s
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