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Block #2,698,754

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/9/2018, 10:24:16 PM Β· Difficulty 11.6468 Β· 4,141,373 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6dcb25c3458342e84f21682fffede916b9c83b44e9c55323dbc889b27331936d
View on Chainz β†—

Height

#2,698,754

Difficulty

11.646790

Transactions

2

Size

7.99 KB

Version

2

Bits

0ba5940a

Nonce

478,304,625

Timestamp

6/9/2018, 10:24:16 PM

Confirmations

4,141,373

Mined by

⛏️ P2SHAQJ6L3JnfgZQqgzkMUvgxDrtTdpz6hMojt

Merkle Root

404e22911b319bc0f0a33bcb3c8d9cd7b174b971a822df3706e24089c226ca6c
Transactions (2)
Coinbase16d7747db0445e…42db1cd558f651
1 in β†’ 1 out7.4400 XPM109 B
AQJ6L3Jn…pz6hMojt
c5bf8224aaa7b4…7b80e24ef3ddc5
69 in β†’ 2 out500.3900 XPM7.80 KB
AJcDB81D…ZX2on3CsAbWzvjG8…Z9zzbHZL
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.

7.534 Γ— 10⁹⁡(96-digit number)
75341995630549515417…01260821729809727999
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
7.534 Γ— 10⁹⁡(96-digit number)
75341995630549515417…01260821729809727999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.534 Γ— 10⁹⁡(96-digit number)
75341995630549515417…01260821729809728001
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
1.506 Γ— 10⁹⁢(97-digit number)
15068399126109903083…02521643459619455999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.506 Γ— 10⁹⁢(97-digit number)
15068399126109903083…02521643459619456001
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
3.013 Γ— 10⁹⁢(97-digit number)
30136798252219806167…05043286919238911999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.013 Γ— 10⁹⁢(97-digit number)
30136798252219806167…05043286919238912001
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
6.027 Γ— 10⁹⁢(97-digit number)
60273596504439612334…10086573838477823999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.027 Γ— 10⁹⁢(97-digit number)
60273596504439612334…10086573838477824001
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
1.205 Γ— 10⁹⁷(98-digit number)
12054719300887922466…20173147676955647999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.205 Γ— 10⁹⁷(98-digit number)
12054719300887922466…20173147676955648001
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
2.410 Γ— 10⁹⁷(98-digit number)
24109438601775844933…40346295353911295999
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:57,965,330 XPMΒ·at block #6,840,126 Β· updates every 60s
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