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Block #455,813

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/22/2014, 7:04:11 PM Β· Difficulty 10.4172 Β· 6,348,084 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d3c116fc2aee7e78e510448b916afe4d2da7e70c5f8ba5dc7d64d239b09c03c3
View on Chainz β†—

Height

#455,813

Difficulty

10.417245

Transactions

2

Size

1.13 KB

Version

2

Bits

0a6ad08a

Nonce

1,493,131

Timestamp

3/22/2014, 7:04:11 PM

Confirmations

6,348,084

Mined by

⛏️ aS-rAbopjr7ZNGrUjb1L7deX9XNozHzLTB81mz

Merkle Root

9df903ef5d42bed7b74e7e1ef993f847dd4854163c3de98e5bc544703f3256b8
Transactions (2)
Coinbase66ce534b57063e…43865695fcef2d
1 in β†’ 1 out9.2000 XPM97 B
Abopjr7Z…zLTB81mz
090019bf761a9d…5c435b4597a2f9
6 in β†’ 2 out26.9861 XPM968 B
ATzMi2JT…Wih7rt49APynswY7…TLf2XCts
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.

5.809 Γ— 10⁸⁹(90-digit number)
58095489452680825502…94290403171457576719
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
5.809 Γ— 10⁸⁹(90-digit number)
58095489452680825502…94290403171457576719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.809 Γ— 10⁸⁹(90-digit number)
58095489452680825502…94290403171457576721
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
1.161 Γ— 10⁹⁰(91-digit number)
11619097890536165100…88580806342915153439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.161 Γ— 10⁹⁰(91-digit number)
11619097890536165100…88580806342915153441
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
2.323 Γ— 10⁹⁰(91-digit number)
23238195781072330201…77161612685830306879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.323 Γ— 10⁹⁰(91-digit number)
23238195781072330201…77161612685830306881
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
4.647 Γ— 10⁹⁰(91-digit number)
46476391562144660402…54323225371660613759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.647 Γ— 10⁹⁰(91-digit number)
46476391562144660402…54323225371660613761
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
9.295 Γ— 10⁹⁰(91-digit number)
92952783124289320804…08646450743321227519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.295 Γ— 10⁹⁰(91-digit number)
92952783124289320804…08646450743321227521
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:57,675,221 XPMΒ·at block #6,803,896 Β· updates every 60s
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