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Block #442,457

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/13/2014, 8:26:30 PM Β· Difficulty 10.3504 Β· 6,366,829 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1c5248a66ca8ec4b89fe96a1eac3f21274bd2cad05400de69de17c170b79900e
View on Chainz β†—

Height

#442,457

Difficulty

10.350392

Transactions

1

Size

207 B

Version

2

Bits

0a59b343

Nonce

843

Timestamp

3/13/2014, 8:26:30 PM

Confirmations

6,366,829

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

896cf24a66282b8d612cc264ae88d80a569901c27d5e51a1be005fc24ca479d3
Transactions (1)
Coinbase896cf24a66282b…005fc24ca479d3
1 in β†’ 1 out9.3200 XPM116 B
AbwWkWZt…kawDhufa
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.

7.322 Γ— 10⁹⁢(97-digit number)
73220857253976597625…14035099605712186999
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
7.322 Γ— 10⁹⁢(97-digit number)
73220857253976597625…14035099605712186999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.322 Γ— 10⁹⁢(97-digit number)
73220857253976597625…14035099605712187001
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
1.464 Γ— 10⁹⁷(98-digit number)
14644171450795319525…28070199211424373999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.464 Γ— 10⁹⁷(98-digit number)
14644171450795319525…28070199211424374001
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
2.928 Γ— 10⁹⁷(98-digit number)
29288342901590639050…56140398422848747999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.928 Γ— 10⁹⁷(98-digit number)
29288342901590639050…56140398422848748001
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
5.857 Γ— 10⁹⁷(98-digit number)
58576685803181278100…12280796845697495999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.857 Γ— 10⁹⁷(98-digit number)
58576685803181278100…12280796845697496001
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
1.171 Γ— 10⁹⁸(99-digit number)
11715337160636255620…24561593691394991999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.171 Γ— 10⁹⁸(99-digit number)
11715337160636255620…24561593691394992001
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:57,718,358 XPMΒ·at block #6,809,285 Β· updates every 60s
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