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Block #1,367,453

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2015, 1:40:27 AM Β· Difficulty 10.8434 Β· 5,437,349 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c860c58c1c460274a636bd612121e6960a332db4f6a2a96ebe53940d8ea1f40
View on Chainz β†—

Height

#1,367,453

Difficulty

10.843373

Transactions

2

Size

7.77 KB

Version

2

Bits

0ad7e74e

Nonce

1,738,279,538

Timestamp

12/13/2015, 1:40:27 AM

Confirmations

5,437,349

Mined by

⛏️ P2SHAcvoAecBKSpfJR1szBQTYywKc98jMR7om4

Merkle Root

dacdab9ef4a3f4036c26e4174222a18972ba8eb8841bd1c77bd0dc41ab99427a
Transactions (2)
Coinbase617982e7c2b6d2…7687319a08014b
1 in β†’ 1 out8.6000 XPM110 B
AcvoAecB…8jMR7om4
a42fcc8889bf62…c2cac0d04dcdf7
52 in β†’ 2 out3305.6091 XPM7.58 KB
AaAs1Tar…MuqwDeTDAQsukK2f…HU9Sfs4E
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.

1.423 Γ— 10⁹⁴(95-digit number)
14230242925146433084…84257238369697437679
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
1.423 Γ— 10⁹⁴(95-digit number)
14230242925146433084…84257238369697437679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.423 Γ— 10⁹⁴(95-digit number)
14230242925146433084…84257238369697437681
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
2.846 Γ— 10⁹⁴(95-digit number)
28460485850292866168…68514476739394875359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.846 Γ— 10⁹⁴(95-digit number)
28460485850292866168…68514476739394875361
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
5.692 Γ— 10⁹⁴(95-digit number)
56920971700585732336…37028953478789750719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.692 Γ— 10⁹⁴(95-digit number)
56920971700585732336…37028953478789750721
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
1.138 Γ— 10⁹⁡(96-digit number)
11384194340117146467…74057906957579501439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.138 Γ— 10⁹⁡(96-digit number)
11384194340117146467…74057906957579501441
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
2.276 Γ— 10⁹⁡(96-digit number)
22768388680234292934…48115813915159002879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.276 Γ— 10⁹⁡(96-digit number)
22768388680234292934…48115813915159002881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,682,483 XPMΒ·at block #6,804,801 Β· updates every 60s
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