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Block #458,779

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/24/2014, 8:10:49 PM Β· Difficulty 10.4213 Β· 6,337,655 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0ccf75bcde918a0c2c8eef97ee22215701ab311984cb192372018661206f1ff5
View on Chainz β†—

Height

#458,779

Difficulty

10.421286

Transactions

2

Size

575 B

Version

2

Bits

0a6bd96b

Nonce

12,596

Timestamp

3/24/2014, 8:10:49 PM

Confirmations

6,337,655

Mined by

⛏️ P2SHAVdBN9t8PCVregLLifpCxkPcdh5jXqqEbP

Merkle Root

34c1dc3e64c54b22ab428b6053f09e6f53e2c4d317636239de7ec7599f452026
Transactions (2)
Coinbase0f83c9c8b4889d…1c19c469783e66
1 in β†’ 1 out9.2000 XPM111 B
AVdBN9t8…5jXqqEbP
8971ae9e164661…c90c27ae891086
2 in β†’ 2 out101.2450 XPM373 B
AR3hpePa…eNN7bKhbAb9z26Uy…4y7ZjJrk
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.

2.213 Γ— 10⁹⁷(98-digit number)
22133828493698351252…79658419804500631659
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
2.213 Γ— 10⁹⁷(98-digit number)
22133828493698351252…79658419804500631659
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.213 Γ— 10⁹⁷(98-digit number)
22133828493698351252…79658419804500631661
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
4.426 Γ— 10⁹⁷(98-digit number)
44267656987396702505…59316839609001263319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.426 Γ— 10⁹⁷(98-digit number)
44267656987396702505…59316839609001263321
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
8.853 Γ— 10⁹⁷(98-digit number)
88535313974793405010…18633679218002526639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.853 Γ— 10⁹⁷(98-digit number)
88535313974793405010…18633679218002526641
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
1.770 Γ— 10⁹⁸(99-digit number)
17707062794958681002…37267358436005053279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.770 Γ— 10⁹⁸(99-digit number)
17707062794958681002…37267358436005053281
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
3.541 Γ— 10⁹⁸(99-digit number)
35414125589917362004…74534716872010106559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.541 Γ— 10⁹⁸(99-digit number)
35414125589917362004…74534716872010106561
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:57,615,464 XPMΒ·at block #6,796,433 Β· updates every 60s
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